Samuel Clemens in Buffalo: A Woman and an Artist Essay -- Samuel Cleme

Samuel Clemens in Buffalo A Woman and an ArtistPreface time literary critics and historians alike have thoroughly examined the influence of Samuel Langhorne Clemens Missouri boyhood and foreign travels on his writing, scholars outside of Western New York consistently overlook the importance of the cardinal months he spent in Buffalo from August 1869 to March 1871. Though a Buffalo resident for the past twenty years, I was also merely vaguely aware that Clemens passed through until Dr. Walter Sharrow of the Canisius College History Department mentioned his local stay. The suggestion that Americas best satirist lived in Buffaloa muddle that could provide a contemporary wit with a wide range of materialtickled my historical sensibilities. Nearly immediately, I began to speculate why Americas most famous writer would migrate to Buffalo. After I discarded my first ideasthe weather, the Buffalo Bills, the efficiency and effectiveness of our local political leadersI concluded it must be because of a woman. Indeed, my early research echoed this assumption, reinforcing my interest in straddles experience here and inspiring the first instalment of this paper. When furthering my research, I developed a second straits of interest. Two local scholars, Martin B. Fried and Tom Reigstad both suggest that Buffalo was a major point of transition for Clemens. Fried writes, His Buffalo experience, scanted in most biographies, has significance because it was the final stage in a long campaign for an artistic existence issue of financial worries and of the burdens of journalistic writing. This suggestionthat his time in Buffalo inspired his development from humorist and journalist to the novelist who produced Huck Finnintrigued me de... ...287_____________. 11 and 13 March 1871.Mark galluss Letters, vol. 4, 349-350.Langdon, Olivia. 17 June 1868. Mark Twains Letters, vol. 2, 286. Twain, Mark. Salutatory, Buffalo Express. August 21, 1869 reprinted in Joseph B. McCullough and Janice McIntire-Strasburg, Mark Twain and the Buffalo Express, 5.Twain, Mark. A General Reply. Buffalo Express. November 12, 1870 reprinted in Joseph B. McCullough and Janice McIntire-Strasburg, Mark Twain and the Buffalo Express, 254.Secondary Sources Martin B. Fried, Mark Twain in Buffalo, Niagara Frontier 5, no. 4 (Buffalo Buffalo Historical Society, Winter 1959) 89.Justin Kaplan, Mr. Clemens and Mr. Twain, (New York Simon and Schuster, 1966), 52.Joseph B. McCullough and Janice McIntire-Strasburg, Mark Twain and the Buffalo Express. DeKalb Northern Illinois Press 1999, xix.

Essay on the Role of Women in Chinua Achebes Things Fall Apart

The Role of Women in Things Fall Apart Chinua Achebes Things Fall Apart explores the struggle between old traditions within the Igbo community as well as Christianity and the second coming it brings forth. While on the surface, it appears the novel narrows its focus to a single character, Okonkno and his inner battles, one can read deeper into the text edition and find an array of assorted conflicts in the realm on human vs. human, human vs. nature, human vs. society, and society vs. society. For the purposes of this paper I shall focus on the internal ear of human vs. human and human vs. society in the framework of the role of women in Igbo society and how men assign and dictate these roles. I will alike briefly explain the importance of women in terms of motherhood and wifedom. Throughout my research Ive encountered numerous papers on the rights women do have in Igbo society, on the importance of women in this society. They site the role of widows in Igbo society as well as t he respect given to the first wife as test copy that while this society is not an ideal situation for women, it is hardly the misogynist society that some make it out to be. I passionately disagree. It is obvious to me that to the characters in Things Fall Apart, women are things to be exploited, abused and to serve as second-class citizens to the rank of male privilege. The theme of misogyny runs rampant throughout the text whether it is undefendable by the absence of women in the text, the abuses women suffer at the hands of men, or the subtle ways in which society dictates and reinforces these negative statuses and images of women. Throughout the text women are virtually invisible and live their lives on the sidelines it is clear from a close read... ...p exclusively be sickened and saddened by not only the reality of women in Africa but of Achebes portrayal of it. Works Cited Achebe, Chinua. Things Fall Apart. London William Heinemann Ltd., 1958. Chun, June. The Role o f Women in Things Fall Apart 1990 October 1999 Jeyifo, Biodun. Okonkwo and his Mother Things Fall Apart and Issues of Gender in the Constitution of African Postcolonial intervention Callaloo Fall 1993 Mezu, Rose Ure. Women in Achebes World Spring/Summer 1995. October 1999 Osei-Nyame, Kwadwo. Chinua Achebe Writing Culture Representations of Gender and Tyranny in Things Fall Apart Research in African Literatures Summer 1999. Sengovaa, Joko. Native Identity and Alienation in Richard Wrights Native Son and Chinua Achebes Things Fall Apart A Cross Cultural Analysis The multiple sclerosis Quarterly Spring 1997.

Evolution, God and Society :: essays research papers

The Island of Dr. MoreauEvolution, divinity and SocietyIn the book The Island of Dr. Moreau by H.G. Wells, we see a microcosm in which Evolution, God and the society are all represented by something strange. First, Dr. Moreau is playing the role of God. Dr. Moreau is an educated man trying to prove that he can turn an sentient being into a human form, so that the animal will forget all of its animal instincts and become more and more human. After Moreau created these beast men, he wherefore controlled them through fear. The fear was of anguish. The house of pain was were the creatures were created and they all remember the pain and therefore associate Dr. Moreau with pain so they do not have to go back. Montgomery played the part of an ignorant assistant. Montgomery was not a stupid man, but he was torn between good and bad, right and wrong, and friendships. I think he tried to play the part of the massager or the son, but he did not agree with what Moreau was doing to the anim als. The Creatures did not respect him the same as Moreau because he had not caused them any physical pain. Montgomery fit in and got along with the beast people more than Moreau did. If he would have stood up to Moreau and made the experiments stop, he then could have been an angle, or a godlier figure. The only thing that kept Montgomery from going crazy was all the alcohol that made his mental pain go num. Then we have Prendick, the voice of reason. Poor Prendick came to the island after being stranded out at see on his little boat. He fancy he was going to die, and his friends and family back at home probably thought he was also dead. But, he was saved by a large boat that Montgomery and normal animals were using to get back to the island. When Prendick steps off the boat onto the island, he can not even begin to understand what creatures are lurking around, some even helping to unload the boat and speaking like humans. Within the first week of being on the island, he knew som ething was wrong and indispensable to be done. Prendick thought that Dr. Moreau was turning humans into animals. This in his eyes was wrong and he was ready to do something about it.

Good and Evil in Quinns Ishmael Essay -- Daniel Quinn essays research

Human beings are destroying the world. Its a fact we all know. Pollution is abundant, we chop down rain forests, we kill our own kind, we steal, lie, and cheat, and the key could go on and on. Daniel Quinn believes that this destruction comes from something more extreme than just the notion to survive. In his novel, Ishmael, Quinn believes that the problems facing humanity are do to mans acquaintance of good and evil.Mans knowledge of good and evil gives us the power to rule the world any way we please. A God or Gods no longer have control. erst Adam, who represents the life of the human race, took a bite from the fruit of the tree of knowledge mans fate was sealed. This knowledge insured, Man was born to rule the world (165). To man this knowledge is the greatest of all. Becau...

Science and African Metaphysics :: Africa Government Papers

Science and African MetaphysicsIf one takes the African situation as a expression study, one finds that serious efforts atomic number 18 made for the sake of scientific progress and exploration. However, the results attained are not comparable to the verve expended. Lack of progress is often attributed to faulty policy defining and execution on the part of African leaders and governments. This essay attempts to shed light on the source of this problem. The heuristic principle I follow holds that the metaphysical preconditioning of consciousness leads us to approach sensory data in particular ways and, furthermore, influences both our formulation of problems and possible solutions. I note the lapses in African metaphysics and sketch an alternate metaphysics which I hope will inaugurate a new African system of thought.INTRODUCTIONThe distinctions Between metaphysics As Body Of Beliefs and metaphysics as a Tool Of Exploration shall serve as the foundation of this essay. The essay wo uld review and highlight some important characteristics of metaphysics as the most fundamental intuition and the basic tool of exploration. This claim, among others, has incidentally been the root of most harsh and destructive criticisms against metaphysics as a ask in futility. (1) These doubts and criticisms notwithstanding the understanding of metaphysics as the throttle valve of scientific progress and exploration would be upheld in this essay. This is borne from the insight that scientific progress is sustained by the urge to go beyond each get-at-able results. To stimulate this urge, whether real, hypothetical or even imaginary would be identified in this essay as the pride of metaphysics. Yet not all quest for quantitative and qualitative scientific growth based on this urge is rewarded with the same amount of progress. If the African situation is taken ask a case study, one discovers that serious and consistent efforts are made within this area to ask questions that go b eyond the possible limits of attainable results. Yet the curious energy expanded within the African context in terms of search for scientific answer to challenging problems does not always seem to have riposte commensurate results as comparable to what is obtainable elsewhere. A pertinent question then is this Why is a quest sustained by the urge towards disruption new grounds fundamentally the same, but the results in terms of tangible or recognisable results remain at variance?TWO MODELS OF METAPHYSICAL headTwo models shall be put up for reflection - the science oriented model and the mythological model.

Science and African Metaphysics :: Africa Government Papers

Science and African MetaphysicsIf iodine takes the African situation as a case study, one finds that serious efforts are do for the sake of scientific progress and exploration. However, the results attained are not comparable to the energy expended. Lack of progress is often attributed to faulty policy formation and exercise on the part of African leaders and governments. This essay attempts to shed light on the source of this problem. The heuristic principle I follow holds that the metaphysical preconditioning of brain leads us to approach sensory data in particular ways and, furthermore, influences both our formulation of problems and possible solutions. I note the lapses in African metaphysics and plan an alternate metaphysics which I hope will inaugurate a parvenu African system of thought.INTRODUCTIONThe distinctions Between metaphysics As Body Of Beliefs and metaphysics as a Tool Of Exploration shall serve as the foundation of this essay. The essay would review and highli ght some important characteristics of metaphysics as the most fundamental science and the basal tool of exploration. This claim, among others, has incidentally been the root of most harsh and destructive criticisms against metaphysics as a quest in futility. (1) These doubts and criticisms notwithstanding the understanding of metaphysics as the catalyst of scientific progress and exploration would be upheld in this essay. This is borne from the insight that scientific progress is sustained by the urge to go beyond each attainable results. To brace this urge, whether real, hypothetical or even imaginary would be identified in this essay as the pride of metaphysics. Yet not all quest for numerical and qualitative scientific growth based on this urge is rewarded with the same amount of progress. If the African situation is taken ask a case study, one discovers that serious and consistent efforts are made within this area to ask questions that go beyond the possible limits of attaina ble results. Yet the curious energy expand within the African context in terms of search for scientific answer to challenging problems does not always seem to have yield equal results as comparable to what is obtainable elsewhere. A pertinent question then is this Why is a quest sustained by the urge towards breaking new grounds fundamentally the same, but the results in terms of tangible or recognisable results remain at variance?TWO MODELS OF METAPHYSICAL INQUIRY two models shall be put up for reflection - the science oriented model and the mythological model.

Disneyland: Now and then

I remember being a child and enjoying the smallest bit of happenings here and there. I remember watching cartoons and laughing cashbox my stomach ached. I remember being impoverished and lively. I remember going to Disneyland. My memories from back then are very clear and crisp in my mind even today. Disneyland is the dream world for kids and a place for perfect retreat. I screwing still think of the day when I was eleven and I was about to see Disneyland for the first time. I couldnt restrain my enthusiasm and excitement as we entered the main gates of the land filled with magic and amazement.Thats how I perceived Disneyland when I was eleven a land of wonders. I couldnt wait to see Mickey and Donald smiling back at me. all told the fun and frolic came alive to me, as I stepped in to the magical land of fairy tale. Today when I think about Disneyland, I do not contemplate it as a magic land or a land of wonders. For me, it is just any other amusement park or theme park, nothing added. But what surprises me is the commission my perception has changed towards the same thing in due course.Disneyland is the same in fact it is believed to bewilder grown for best in these years. But for me, it no monthlong remains a place of magic or enchantment. It only tells me one thing, I have moved furthest ahead and my childhood is still behind, lost in the memories of Disneyland. Disneyland meant to me, making the world of animation and cartoon come alive. Mickey Mouse, Donald Duck, Goofy and Bugs Bunny were one of my front-runner cartoon characters ever and watching them alive was like a dream come true.I remember being excited by the thought of seeing those characters in front of me. Like, when I was eleven, I ran with exhilaration to shake hands with the leg quitary Mickey Mouse. I couldnt let his hand go moreover, I hugged him and kink into his arms like he was my teddy bear. I asked my dad to take bundle of pictures with Mickey and Donald. Later, I framed thos e photographs and hung them up on the wall of my room. Moreover, for a long time, I thought of the moment I met Mickey, when I watched cartoon back at home.However, today, when I think of it, I feel a trace of embarrassment. I would never hug Mickey Mouse or Donald Duck for that matter. Although, sometimes, I watch Mickey Mouse and Donald Duck cartoons on television, I do not think of those characters as real cartoons. I understand the fact that they are real people under the disguise of these famous cartoons trying to butterfly kids and entertain them to their best. I feel taking pictures with them as a laughable act and something only kids would want to do.My excitement level is as normal as it would be when I am at home, watching those cartoons. Additionally, when I first went to Disneyland Park, I had enjoyed and jumped in high spirits even for the all the small rides. The illuminance circus train with cars designed as wild animal cages, the crazy tea cup ride, the chip and d ale tree house, exploring Goofys house, the flight to fantasyland with jumbo, the delightful go round, all made me roar out in laughter and eventually, I enjoyed every bit of my ride.The rides were long, simple but very enchanting. The joy arrange in those simple things was incomprehensible and ceaseless. The moments seemed to be so prized and exceptional, that even a camera couldnt bind it in its flashlights and tape. When compared to the latest trip, the experiences, however, beg to differ. The rides seem to be ordinary, just like any other ride, in another amusement park. Every ride tries to test the patience by making us stemma from huge heights, in dangerously simulated situations and backgrounds.All thrill rides seem to endow with higher risks, higher heights, more velocity and more twists. Even after covering a single ride of few minutes of length, there is no sense of delight or bliss. The feeling of joy in the small things seems to have lost. Its just not about having f un anymore. It is only about moving from one ride to another, trying to finish as many rides as possible. Furthermore, when I was young, I remember being excited about the main street parade. I was so keyed up to watch the parade that I blocked seats an hour before the parade actually began.I was overwhelmed with the stunts and cognitive operations of all the characters. Consequently, I struck my eyes all along, without moving an inch. I waited till the end of the parade and not for a moment, thought about leaving early. Each character performing in the parade was special in its own way and I admired them all equally. Nonetheless, now when I think of it, it doesnt seem to be as astonishing as before. Even though the performance of the artists remains of high caliber and incredible excellence, I do not seem to be attracted towards it.I remember the last time I visited Disneyland, my concerns were more towards control back home. I didnt want to block seats an hour before neither did I want to stick till the end. I was acquire late and I was more worried about the traffic. As a Conclusion, I believe that things change with times. Also, the way we perceive things, changes with changing times. When we are young, innocent children, we are ignorant to worries and responsibilities. Also, life seems much dreamier and everything looks like a play area.As we grow older, we seem to intertwine in the complications of life and start losing the small joys we can experience in moments of life that may seem insignificant and diminutive. The moments that are filled with immense joy and blissful entertainment are no longer observed. Life becomes dissolute with growing age and even a beautiful thing passes by, without being noticed. A place like Disneyland, that meant so much to me at one time in my life, no longer holds the meaning it used to. I seem to have lost my innocent childhood in the fast life, in the race to achieve something more.

Mill individuality essay Essay

Within nerds On Liberty it is clear that he has a in high spirits regard for the issues surrounding license and its limits. Mill is an advocate of negative freedom, as a liberal he believes that there should be no restraints on an individuals freedom unless it is hindering the freedom or health of anformer(a) person. One of the main reasons as to why Mill values intimacy is because it contributes to personal development. Thus Mill argues that in say for individuals to develop they should be able to perform experiments in living, which allow individuals to go through a system of trial and error until they find their bear appropriate way of life.Moreover, experiments in living argon beneficial to alliance as they provide a unlike way of living different from that of custom and help tackle the tyranny of overt opinion. Thus it drive out therefore be argued that Mills calculate on personal acquaintance does in fact ascertain the development of inn and the individual. The fir st way in which Mills account of freedom ensures the development of the individual and club, is that it promotes the truth. The link between personal freedom and truth is wizard of bouncy importance to Mill.Personal liberty allows people to observe to opinions and ideas that that they can then go and shargon and spread with other individuals. Thus creating a pluralist society whereby ideas are tolerated, by virtue of them being expressed. In order to create such a society geniuses are needed to introduce new ways of thinking into society and to challenge the old ways of life. For such people to exist we need freedom in society to practice our individuality.Mill states that even if an opinion or individual lifestyle is anomalous or offensive it should be allowed to be expressed, as it will have strengthen the neat opinion or right way of life and allow those dimension that opinion to have greater faith in it. For example, a scientist needs the freedom to experiment in order t o discover new truths about the born(p) world and share these ideas with the rest of humanity. However, should we express discoveries that are wrong? Surely this would be a waste or time.Mill would argue that because even false options have value, we should allow them to be expressed. A false discovery could spur on others to be clearer about what the truth might be, it could even be a step that we take to discover the real truth. Mill does not think that once truth or a good way of individuality is discovered, we should watch complacent with it. This would allow society to be specifym stagnant and proven truths could develop into custom. This would therefore be detrimental to human individuality as individuals will become sheeps and draw custom blindly.Custom does not educate or improve an individuals well being, indeed Mill argues that he who does anything but follow custom, pull outs no choice Mills solution to this is to revisit and reconsider truths, so that they remain li vely. It is in addition true that by not reconsidering customs and public opinions, they could come to rule society, resulting in a mediocre society. Only if there is individual freedom, we can avoid truths becoming dead dogma. If personal liberty did not exist, society would become stagnant and individuals would not question the ways of life around them, meaning that neither society nor individual develop.It is therefore vital to have personal freedom so that individuals are allowed to question ways of life and society can develop. Mill also believes that personal freedom is main(prenominal) because it promotes individuals with a means to develop on a personal level. Mill believes without experiments in living human beings lose what it means to he truly human. In order to be truly human, an individual needs to interpret and adapt the experiences of others and themselves to suit their confess moral codes.Individually is the development and expression of wholenesss own character, as opposed to going along with customs and traditions imposed on society from previous generations. Mill illustrated this himself in the example he gives about Christianity, arguing that the Christian moral system cannot be derived from the New Testament alone, there are also ideas from the Old Testament. This therefore implies that much corresponding the Christian tradition, individuals should derive their own individuality from previous experiences, until now experiment with it so that it is their own private morality.Mill approvingly quotes the German politician Von Humboldt who argues that each persons vision of morality is the intimately harmonious development of his powers to complete a consistent whole. Each persons powers are different, as are there desires and emotions which need to be developed to be complete and consistent. Therefore each persons development is individual to them, thus following custom or public opinion stagnates their individual growth, as they are nit experimenting their faculties.However, it would be easy to criticise this, what if someone elses individuality and experiments in living intermeddle or undermine my way of experimenting. Mill would simply maintain his harm dominion to such a situation. As long as my way of life does not harm or infringe on other peoples rights and their own freedom then I am allowed to act on any way that pleases me. It can be argued that such a restraint protects society from damaging behaviour but also improves me as a person as I am not indulging in selfish acts. indeed it is beneficial to society to have eccentricity, because without it, it can be argued that people will become submissive, weak willed and without strong opinions. Society will lose it means to cash advanceing further. Mill talks about this to am extent in his chapter on democracy. He argues that in order for society to develop we need two opposing parties, one that is defined by tradition and pragmatism and the other by s ocial progress. However, it can be argued that by giving people the means to be eccentrics you are threatening social order and putting society at whole at a risk ( the opposite of what Mill says his theory does).However , like most problems that surround the idea of negative liberty, mill would argue that as long as the experiment in living is within the limits of the harm regulation them it should be allowed. This personal liberty not merely provides people with a means to experiment their own ways of living, but also allows society to exposit as eccentricity and geniuses (provided by liberty) can enlighten individuals and governments into new ways of living. Furthermore, to treat human beings with no individuality and not provide them with a means of experimenting in their living, is to assume that they are all the same.Mill argues that we are all different in our desires and in what will make us happy. Imposing a particularized lifestyle on all members of society would be li ke treating an orchid, sunflower and cactus all in the same way. The conditions in which the orchids thrive could kill the sunflower. Much like plants, human beings differ too much to attempt to make all members of society conform to one model of the good life. However, speaking from a redness perspective we could argue that human beings should only focus on need satisfaction.This would mean that all individuals have the same needs such as food, water and shelter. Marx argued that in order to live a true human existence, human beings should focus on satisfying those needs equally. Therefore, Mills line of products that individuals are different would prove to be invalid to Marx. Although Marx makes a valid point, it would be in cohesive to argue that all human beings do in reality have the same needs. For example, someone with disabilities is going to have more needs than a non disabled person.Thus it is true that different human beings have different needs in order to create thi s individual identity. How can society progress if all human beings are treated the same? Surely it is only because of difference in ideas that human human being have come so far. To treat a hard working person the same as a lazy person seems unjust, their individuality is different and their desires too are different. Treating them the same would not amount to higher levels of liberty. Thus personal liberty does ensure developments in society and the individuals.One of the main objections to Mills individuality argument is that there are many situations in which utility may encounter with individual freedom. The idea that utility and conflict can conflict is illustrated by the potential drug addict. If a state prevents an individual from buying an extremely addictive drug, for example heroin, although we take away their individual freedom we are also contributing to their utility, and the utility of others as taking drugs can affect others indirectly.The harm principle is difficu lt to apply in such a situation, because it implies that only acts that are infringing on the liberty of another person or causing them harm should be stopped. Therefore it can be argued that society needs a source of paternalism. Conservatives argue that Mill has given human beings more rationality than they really possess. Conservatives see human beings as rationally imperfect creatures who need guidance. Mill gives special emphasis to the faculty of reason. For Mill it is reason that enables us to use our liberty effectively and even improve it.Conservatives to argue that there us too much weight given to human reason and not enough emphasis on their other characteristics. Although Mill does mention the importance of desires and impulses he assumes that reason can be the way in which we control them. Human beings ,as imperfect creatures, are goaded more by hate, jealousy, sexual desire than they are by reason, if we take these irrational human drives into account, it may be nece ssary to consider restricting freedom in specific areas that mill would not accept, for example their sexual lives.Without such paternal restraints it can be said that individuals will cause harm to themselves and also to society. Therefore no one benefits from personal liberty, instead people are at a disadvantage from it. An argument is given by Lord Devlin as to why personal development could be dangerous of the moral frameworks of society. Devlin argued against the harm principle and negative freedom in the 1950s, during the time of the Wolfenden report, which argued that the law should not interfere with the private lives of its citizens.However Devlin argued that if the law failed to enforce common moral values, society would begin to disintegrate. To sum up Devlins argument, he argued that im order for society to be stable there needs to be a common morality which is public, and not private, it is the governments responsibility to ensure that the welfare of society is looked after, so it is legitimate that governments can pass paternal laws, on the basis of presenting moral values. An example that Devlin uses for his public morality is one of the rum man.Say a man is to get drunk every night on the private sphere of his own home, it can be argued that as long as the man isnt harming society he is free to do this. However what if a quarter of the population is getting drunk every night, that will have negative effects on society and peoples individuality. So society should not tolerate practices that conflict with these common moral values. If these common moral values were aimed at preventing harm to others then Mill would agree, however Devlin was someone who disapproved of self actions, for example drunkenness and homosexual activity.He appeals to social utility and the importance of social cohesion as a way to make society a better place. However is Devlin right to say that actions such as homosexuality lead tot he break down of society? Society had now come to accept legally homosexuals, and society has not broken down. Moreover, how are individuals and societys expected to make moral progress without being allowed to experiment with different practices. Should we really give up the prospect of a developed tolerant society in the name of cohesion, whereby everyone is following one set of rules?To conclude Mills account of personal liberty ensures the development of individuals and society, by allowing the truth to come forward and allow individuals to use their own reason to choose their own ways of life. Society is protected from following custom and becoming stagnant, and also becomes more tolerant to absurd ideas. It is also true that personal liberty is needed so that society can progress into greater things. For example it would be easy to regard feminist and gay thighs thinkers as geniuses as they have pioneered some of the more equal and tolerant laws of this day and age.

The Poison of Human Relationships

My wifes jealousy is getting ridiculous. The other day she odored at my calendar and wanted to know who May was(Dangerfield, 2007)This is a quotation from Rodney Dangerfield and it is quote evident that jealousy makes a relationship crucial and impractical. Crucial in a sense that peoples life elusive in a relationship is affected and it seems that they become such paranoids. It is Impractical be find it really changed atomic number 53s way of living including societal and personal development. fly the cooping is the one acting behind the strings in jealousy. Jealousy is a state, wherein a person experiences fear, suspicion or envy cause by a real or imagined threat or challenge to ones possessive instincts (Webster, 2007). Jealous feelings come up because we are afraid of not getting our needs. close to of the times, we want to be secured of something.We are afraid of being abandoned, of losing ones rawness and love. We are afraid of being abandoned, of losing ones affection and love. We are afraid of unresolved issues from past relationships. Whenever we are jealous of something or of someone, all that we hear is our self. We become deaf of other peoples explanation. We tend to think and see only the negative side of the story. Its been an experience that when jealousy comes up, we pity ourselves. We often think that he or she is far give away than us. Jealousy is a double edged sword, with the sharper edge pointed towards ones self.Jealousy is like a poison which spreads throughout the body and bear upon everything that it makes contact with. Jealousy often is the result of not feeling good about yourself physi thinky and personally. It weakens our emotional well being. At the same time, it builds paranoia to those who are soft on(p) by it. Jealousy, as stated earlier is sort of a poison that paralyzes all the aspects of a human being.Jealousy is a state by which a person feels that he/she should be the one who experiences what another person is g iving to a different person besides himself/herself. Jealousy present even among family members. A good example would be is when a parent does favor for one if their children but not to the other.While this type of jealousy can be lessen if the parent of the child also gives favors to the child that feels jealous, this whitethorn not be the case of a jealous lover. Instead, jealousy is often expressed as anger, ahead(p) us to accuse our partner of cheating. Sometimes those who are eaten by their own jealousy even avoid their friends that have something to offer than you wish you had to your loved ones.Most of the time, jealousy is really about feeling threatened that our relationship will be affected by another person or other situationors. This often results when one does not feel worthy in a relationship. There is always this thinking that ones partner has a reason to look elsewhere for attention because one is not good enough.If the person is a friend, then this also involves betrayal, and the hatred may breed between the two agent friends. Most of us, when in this situation, are blinded by jealousy. Without knowing the main reason or cause of such situation, we easily conclude and usually, our conclusions lead to a fight or to an argument.We often say that love is blind, but sometimes it is not love that makes us blind but jealousy. Being jealous usually arises from the assumption that you own and want to control another persons affection and love and want to keep them all to ones self. This is what we call a conditional love, the person will love another if and only if the other person loves him/her.Jealousy affects health of those stricken by it, aside from the fact that it ruins ones relationship. Feelings of jealousy can consume a persons heart making the person irritable and annoyed . It can cause sleepless nights and lack of appetite. Some even turn to alcohol or drugs to deal with their feelings.While others say that jealousy eats relationship alive and offers zilch in return, some believe and claim that being jealous sparks passion and romance. Jealousy can even sometimes strengthen a relationship. It sometimes sum that you really love that person, that you really care for him/her and you only dont want to loose him/her. Though jealous feelings can be frustrating, annoying and painful, in some way it brings up the feeling of sensual happiness. A little jealousy can sometimes help a relationship grow for the better. Too much of anything is foul to a relationship.Some scientists and researchers believe jealousy can be genetic. Culture and upbringing play a role in jealousy as well. For example, a violent boyfriend may claim his jealousy as the result of loving her partner so much, when in fact in reality, he may be copying the behaviors of his own father and does no know how else or how it is to deal with jealousy.If jealousy is an issue in ones life, understanding of ones behavior and whats underneath it is essential in dealing with jealousy and preserving mental well being as well as the pure tone of relationships.ReferenceQuotes about jealousyhttp//www.worldofquotes.com/topic/Jealousy/1/index.htmlDefinition of JealousyWebster Dictionary.

Ethics in Intelligence Essay

On a clear, late summer day in September of 2001, the hectic yet peaceful lower portion of Manhattan, smart York City was turned into the site of one of the largest mass murders in world history when terrorist attacks turned the once imposing World Trade Center compound to a smoking pile of debris and left thousands of Americans dead, physically and psychologically scarred for life. In the aftermath of this act of aggression, the United States, with the cooperation of allies around the world, launched information collection efforts on a scale that had never before been seen.Some nations would be able to do so as they wished without regard for the privacy or rights of their people, but for a nation conceived in liberty and human rights as the US was, discovers of ethics and the preservation of individual rights had to be balanced against the dire deficiency to protect the masses from further violence. This research will focus on the ethics of comprehension collection in the US, Constitutional implications of these efforts for American citizens, and the consideration of how often liberty US citizens should be willing to give oneself up for the greater good.Ethics of Intel Collections, Means and Methods Intelligence gathering has always been an essential part of the preservation of American warrantor, dating back to the days of the American colonies and beyond. In the late 1990s, for all of the violence brewing in former(a) nations and the potential for domestic terrorism in the US, the intelligence gathering efforts of American officials consisted mostly of the analysis of data from the comfort of offices located in the US and some offices scattered across the globe.However, these efforts were initially be to be weak by international terrorist acts against American military installations in other nations, and the original emergence of Osama Bin Laden as an international terrorist to be closely monitored. With such formidable enemies to consider, it beca me obvious that the old ways of gathering intelligence were badly in need of change, including the entryway of more field intelligence agents, enhancements to technology, better networking with other nations, and many clandestine activities.With the need to increase and improve all levels of intelligence gathering in the US, the question arises as to how far a nation like the US, which die hards as a beacon of righteousness and base hit in the world, will be willing to go to gain the level of security that is needed to protect American citizens at home and abroad? The child of this need emerged, known as the Department of Homeland security measures, an organization which put on a public front of protection of the US in a manner that is illustrative of ethical behavior and forceful yet proper action.With the introduction of the Department, the public gained a higher level of confidence in the protection they would be receiving. However, many of the methods that were necessary, a t least behind the scenes, were of the nature that the general public would frown upon at the very least, and rise up in heated protest against at worst if it were known the full extent of what the Department was obligate to resort to in the interest of intelligence gathering.Among the steps that were taken, such actions as the monitoring of telephone and Internet communications, the detention of suspected terrorists and the like began to raise the issue of the appropriateness of such activities in line with the promises and obligations of the US Constitution. Constitutional Implications of United States Intel Collection on United States CitizensThe war against terrorism is unlike any other war that the US has seen fighting an enemy that does not wear a recognizable uniform or hails from any specific geographic location poses quite an a challenge and makes the application of conventional warfare tactics all but impossible. Therefore, as with those conventional warfare methods, it is necessary for certain drastic measures to be taken.However, it is important to understand that there are Constitutional implications for such actions, especially in the areas of intelligence collection which require frequent intrusions into the privacy that Americans hold so dear and have fought and died to protect for hundreds of years. First, there are misconceptions about the Constitution that are necessary to point out.Specifically, there is a thin line amidst the investigation of criminal activity and suspected threats to national security, which of course are in and of themselves criminal but take on an added dimension when one realizes that the safety and future of the nation hangs in the balance. In the interest of national security, it is permissible for the surveillance of Americans, domestically and abroad without the obtaining of search warrants, which are usually the standard surgical procedure when an American is being investigated as a possible criminal, under an y ordinary circumstances.In this instance, permissible and acceptable are two entirely diametrical things. While authorities may be allowed to basically spy on their fellow citizens so that the nation is protected, where does this leave those who are the target of the surveillance? The descent can fairly be made that if one is not doing anything wrong, if they are being monitored, they actually have nothing with which to be concerned. Further, if that surveillance yields information on other wrongdoers who are in fact a threat to America, the net result makes all of it worthwhile.The issue of habeas corpus also is a key gene in the consideration of the rights the accused. In the past, this legal remedy, in place since the days of the Magna Carta, existed to protect the rights of the accused. Constitutionally speaking, it had been established in the early 1940s that habeas corpus would stand if (1) the credit is void for lack o f personal or subject matter jurisdiction (2) the st atute defining the offense is un built-in, or the conviction was obtained in violation of a federal constitutional right(3) the statute authorizing the sentence is unconstitutional, or the sentence was obtained in violation of a federal constitutional right (4) the sentence is contrary to the applicable statute, in excess of the statutory maximum, or otherwise unauthorized by law or (5) the conviction or the sentence is otherwise deemed subject to collateral attack. In times of crisis, this right has been suspended in the interest of national security, and has been suspended in the age of terrorism due to the need to make terrorists who are evading capture by authorities accountable in courts of law for their crimes.This, also, however is one of those fine points of law that destiny criticism and scrutiny in many cases because anytime a right is suspended, innocent people are affected and their rights are often sacrificed, albeit for the sake of the common good. A closer look at t he underpinnings of the Constitution itself reveals some interesting powers that many do not realize exist. For example, the Constitution does in fact give sexual intercourse the right to make laws as necessary to allow the Constitution to function as it was intended.This right, however, is akin to a broad stroke of a paintbrush, when the finer expatiate of the stroke are really where the beauty lies. In other words, on the surface, it is true that Congress possesses such power, but this is also a power that is have to interpretation and debate. Where one draws the line in the midst of permissible monitoring and the trampling of the rights of the majority is an issue with which the American people are currently wrestling and doubtless will continue to do so for many years to come.With this in mind, there surely must be a balance to be obtained between sacrificing for the common good and giving up everything that Americans are constitutionally guaranteed. How Much Liberty Should US Citizens Give Up Under the Notion of National Security? It has been said that liberty is something which can be gained all at once, but often is stripped away one small piece at a time, like the gradual erosion of a mighty ascentain. If this is true, the question of how many small pieces the citizens of the US can give away before a landslip consumes them?After the horrible events of September 11, 2001, it became readily apparent that there was a need for American governmental agencies to gather additional power if they were to properly mount an offensive against terrorism and to avert a repeat of the horrible events of that tragic day. This need to gather additional power was viewed by many as a feeble excuse for those within the government who craved power to grab as much as they wished, regardless of the inevitable fallout.Still others saw the sacrifice of a small amount of liberty as the necessary toll that needed to be paid for a much larger amount of general protection a nd the long-term survival of the US while others around the world plotted to destroy the most powerful nation on earth. Again, however, as was mentioned at the beginning of this passage, small surrenders can sometimes lead to large damage over a period of time.

Financial Management Essay

Question 1-3Suppose three h one(a)st individuals gave you their estimates of Stock Xs intrinsic value. One is your current roommate, the second is a headmaster security analyst with an excellent reputation on Wall Street, and the third is Company Xs CFO. If the three estimates differed, in which one would you have the most confidence? Why?Question 1-7Should stockholder wealth maximization be thought of as a long-term or short-term goal? For example, if one action increases a firms stock price from a current level of $20 to $25 in 6 months and then to $30 in 5 years but another action keeps the stock at $20 for several years but then increases it to $40 in 5 years, which action would be better? Think of some specific corporate actions that have these general tendencies.Question 1-9The president of Southern Semiconductor peck (SSC) made this statement in the companys annual report SSCs primary goal is to increase the value of our common stockholders equity. Later in the report, the f ollowing announcements were made a. The company contributed $1.5 million to the symphony orchestra in Birmingham, Alabama, its headquarters city. b. The company is spending $500 million to open a new coif and expand operations in China.No profits will be produced by the Chinese operation for 4 years, so earnings will be depressed during this period versus what they would have been had the decision been made not to expand in China. c. The company holds about half of its assets in the form in U.S. treasury bonds, and it keeps these funds available for use in emergencies. In the future, though, SSC plans to shift its emergency funds from Treasury bonds to common stocks.

Mlc Cheat Sheet

mkThis p time intentionally left blank Actuarial Mathematics for Life depending on(p) Risks How limitinate actuaries best equip themselves for the masterducts and run a happen structures of the proximo? In this new text keep punt, deuce-ace leaders in actuarial science give a go on perspective on carriage contingencies. The book begins traditionally, c everywhereing actuarial models and system, and emphasizing practical applications victimisation computational techniques. The authors then develop a much mod-day outlook, introducing multiple state models, emerging currency ? ws and embedded plectrums. Using spreadsheet-style softw be, the book presents hulking-scale, pictorial examples. Over 150 good examples and solutions t to to each one one skills in simulation and projection by means of computational practice. Balancing rigour with intuition, and emphasizing applications, this textbook is ideal not only for university courses, barely as well for individua ls preparing for professional actuarial examinations and quali? ed actuaries wishing to transmig situate and update their skills.International Series on Actuarial Science Christopher Daykin, Independent Consultant and Actuary Angus Macdonald, Heriot-Watt University The International Series on Actuarial Science, published by Cambridge University Press in conjunction with the Institute of Actuaries and the Faculty of Actuaries, contains textbooks for students taking courses in or related to actuarial science, as well as more advanced works intentional for continuing professional development or for describing and synthesizing research.The series is a vehicle for publishing books that re? ect changes and developments in the curriculum, that encourage the fundament of courses on actuarial science in universities, and that show how actuarial science weed be employ in all atomic physique 18as where in that respect is long- precondition ? nancial risk. actuarial MATHEMATICS FOR LIF E CONTINGENT RISKS D AV I D C . M . D I C K S O N University of Melbourne M A RY R . H A R D Y University of Waterloo, Ontario H O WA R D R . WAT E R S Heriot-Watt University, Edinburgh CAMBRIDGE UNIVERSITY PRESSCambridge, New York, Melbourne, Madrid, Cape Town, Singapore, Sao Paulo, Delhi, Dubai, Tokyo Cambridge University Press The Edinburgh Building, Cambridge CB2 8RU, UK Published in the United States of America by Cambridge University Press, New York www. cambridge. org Information on this title www. cambridge. org/9780521118255 D. C. M. Dickson, M. R. Hardy and H. R. Waters 2009 This publication is in copyright. Subject to statutory ejection and to the provision of relevant collective licensing agreements, no reproduction of any vox whitethorn puzzle place without the written permission of Cambridge University Press.First published in print format 2009 ISBN-13 ISBN-13 978-0-511-65169-4 978-0-521-11825-5 eBook (NetLibrary) Hardback Cambridge University Press has no responsi bility for the persistence or accuracy of urls for external or third-party internet websites referred to in this publication, and does not guarantee that any content on much(prenominal) websites is, or impart remain, accurate or appropriate. To Carolann, Vivien and Phelim Contents Preface page xiv 1 macrocosm to bread and butter damages 1 1. 1 abstract 1 1. 2 Background 1 1. 3 Life indemnification and rente contracts 3 1. 3. 1 gate 3 1. 3. conventional indemnity contracts 4 1. 3. 3 Modern restitution contracts 6 1. 3. 4 Distribution methods 8 1. 3. 5 Underwriting 8 1. 3. 6 bounteousnesss 10 1. 3. 7 Life annuities 11 1. 4 Other damages contracts 12 1. 5 indemnity bene? ts 12 1. 5. 1 De? ned bene? t and de? ned contribution awards 13 1. 5. 2 De? ned bene? t premium design 13 1. 6 Mutual and copyrighted insurance firms 14 1. 7 Typical problems 14 1. 8 Notes and further read 15 1. 9 Exercises 15 2 Survival models 17 2. 1 abstract 17 2. 2 The future action clipping random variable 17 2. 3 The force of expirationrate 21 2. 4 Actuarial notation 26 2. smashed and streamer deviation of Tx 29 2. 6 Curtate future tone-timetime 32 2. 6. 1 Kx and ex 32 vii viii 2. 6. 2 Contents The perfect(a) and curtate expected future ? invigoration generation, ex and ex 2. 7 Notes and further culture 2. 8 Exercises Life tables and selection 3. 1 Summary 3. 2 Life tables 3. 3 Fractional age presumptions 3. 3. 1 Uniform distribution of finiss 3. 3. 2 invariant force of mortality 3. 4 National conduct tables 3. 5 Survival models for make loveness indemnification polityh ho bers 3. 6 Life redress underwriting 3. 7 Select and ultimate survival models 3. 8 Notation and formulae for select survival models 3. Select demeanor tables 3. 10 Notes and further reading 3. 11 Exercises Insurance bene? ts 4. 1 Summary 4. 2 induction 4. 3 Assumptions 4. 4 rating of indemnification policy bene? ts ? 4. 4. 1 Whole disembodied spirit indemnification the contin uous case, Ax 4. 4. 2 Whole sustenance policy the annual case, Ax (m) 4. 4. 3 Whole life restitution the 1/mthly case, Ax 4. 4. 4 Recursions 4. 4. 5 Term insurance 4. 4. 6 Pure talent 4. 4. 7 Endowment insurance 4. 4. 8 Deferred insurance bene? ts (m) ? 4. 5 Relating Ax , Ax and Ax 4. 5. 1 Using the uniform distribution of deaths assumption 4. 5. 2 Using the claims acceleration approach 4. Variable insurance bene? ts 4. 7 Functions for select lives 4. 8 Notes and further reading 4. 9 Exercises Annuities 5. 1 Summary 5. 2 Introduction 3 4 34 35 36 41 41 41 44 44 48 49 52 54 56 58 59 67 67 73 73 73 74 75 75 78 79 81 86 88 89 91 93 93 95 96 one hundred one 101 102 107 107 107 5 Contents 5. 3 5. 4 Review of annuities- plastered Annual life annuities 5. 4. 1 Whole life rente-due 5. 4. 2 Term rente-due 5. 4. 3 Whole life immediate annuity 5. 4. 4 Term immediate annuity 5. 5 Annuities compriseable continuously 5. 5. 1 Whole life continuous annuity 5. 5. 2 Term continuous annuity 5. 6 Annuities collapseable m times per year 5. . 1 Introduction 5. 6. 2 Life annuities payable m times a year 5. 6. 3 Term annuities payable m times a year 5. 7 Comparison of annuities by allowance frequency 5. 8 Deferred annuities 5. 9 Guaranteed annuities 5. 10 Increasing annuities 5. 10. 1 Arithmetically increasing annuities 5. 10. 2 Geometrically increasing annuities 5. 11 Evaluating annuity functions 5. 11. 1 Recursions 5. 11. 2 Applying the UDD assumption 5. 11. 3 Woolhouses formula 5. 12 Numerical illustrations 5. 13 Functions for select lives 5. 14 Notes and further reading 5. 15 Exercises Premium calculation 6. 1 Summary 6. 2 Preliminaries 6. Assumptions 6. 4 The present value of future loss random variable 6. 5 The equivalence principle 6. 5. 1 Net agios 6. 6 Gross premium calculation 6. 7 Pro? t 6. 8 The portfolio percentile premium principle 6. 9 Extra risks 6. 9. 1 Age rating 6. 9. 2 Constant addition to x 6. 9. 3 Constant multiple of mortality place ix 108 108 109 112 113 114 115 115 117 118 118 119 120 121 123 125 127 127 129 130 130 131 132 cxxxv 136 137 137 142 142 142 143 145 146 146 150 154 162 165 165 165 167 6 x Contents 6. 10 Notes and further reading 6. 11 Exercises Policy values 7. 1 Summary 7. 2 Assumptions 7. Policies with annual cash ? ows 7. 3. 1 The future loss random variable 7. 3. 2 Policy values for policies with annual cash ? ows 7. 3. 3 Recursive formulae for policy values 7. 3. 4 Annual pro? t 7. 3. 5 Asset sh atomic number 18s 7. 4 Policy values for policies with cash ? ows at distinguishable intervals other than annually 7. 4. 1 Recursions 7. 4. 2 Valuation amid premium dates 7. 5 Policy values with continuous cash ? ows 7. 5. 1 Thieles diverseial equation 7. 5. 2 Numerical solution of Thieles differential equation 7. 6 Policy alterations 7. 7 Retrospective policy value 7. 8 contr everywheret policy values 7. Notes and further reading 7. 10 Exercises Multiple state models 8. 1 Summary 8. 2 Examples of multiple state models 8. 2. 1 The alive light model 8. 2. 2 Term insurance with increased bene? t on accidental death 8. 2. 3 The permanent constipation model 8. 2. 4 The disability income insurance model 8. 2. 5 The joint life and last subsister model 8. 3 Assumptions and notation 8. 4 Formulae for probabilities 8. 4. 1 Kolmogorovs forward equations 8. 5 Numerical evaluation of probabilities 8. 6 Premiums 8. 7 Policy values and Thieles differential equation 8. 7. 1 The disability income model 8. 7. Thieles differential equation the general case 169 170 176 176 176 176 176 182 191 196 200 203 204 205 207 207 211 213 219 220 220 220 230 230 230 230 232 232 233 234 235 239 242 243 247 250 251 255 7 8 Contents 8. 8 8. 9 Multiple decrement models Joint life and last survivor bene? ts 8. 9. 1 The model and assumptions 8. 9. 2 Joint life and last survivor probabilities 8. 9. 3 Joint life and last survivor annuity and insurance functions 8. 9. 4 An important special case independent survival models 8. 10 Transitions at speci? ed ages 8. 11 Notes and further reading 8. 12 Exercises Pension mathematics 9. Summary 9. 2 Introduction 9. 3 The requital scale function 9. 4 Setting the DC contribution 9. 5 The advantage table 9. 6 Valuation of bene? ts 9. 6. 1 Final pay plans 9. 6. 2 C areer number earnings plans 9. 7 Funding plans 9. 8 Notes and further reading 9. 9 Exercises Inte break rate risk 10. 1 Summary 10. 2 The yield curve 10. 3 Valuation of insurances and life annuities 10. 3. 1 Replicating the cash ? ows of a traditional non-participating product 10. 4 Diversi? able and non-diversi? able risk 10. 4. 1 Diversi? able mortality risk 10. 4. 2 Non-diversi? able risk 10. 5 Monte Carlo simulation 10. Notes and further reading 10. 7 Exercises Emerging be for traditional life insurance 11. 1 Summary 11. 2 Pro? t scrutiny for traditional life insurance 11. 2. 1 The net cash ? ows for a policy 11. 2. 2 Reserves 11. 3 Pro? t measures 11. 4 A further example of a pro? t test xi 25 6 261 261 262 264 270 274 278 279 290 290 290 291 294 297 306 306 312 314 319 319 326 326 326 330 332 334 335 336 342 348 348 353 353 353 353 355 358 360 9 10 11 xii Contents 11. 5 Notes and further reading 11. 6 Exercises Emerging costs for equity-linked insurance 12. 1 Summary 12. 2 Equity-linked insurance 12. 3 Deterministic pro? testing for equity-linked insurance 12. 4 Stochastic pro? t testing 12. 5 Stochastic price 12. 6 Stochastic reserving 12. 6. 1 Reserving for policies with non-diversi? able risk 12. 6. 2 Quantile reserving 12. 6. 3 CTE reserving 12. 6. 4 Comments on reserving 12. 7 Notes and further reading 12. 8 Exercises Option pricing 13. 1 Summary 13. 2 Introduction 13. 3 The no arbitrage assumption 13. 4 Options 13. 5 The binomial option pricing model 13. 5. 1 Assumptions 13. 5. 2 price over a single time period 13. 5. 3 Pricing over two time periods 13. 5. 4 Summary of the binomial model option pricing technique 13. The BlackScholesMerton model 13. 6. 1 The model 1 3. 6. 2 The BlackScholesMerton option pricing formula 13. 7 Notes and further reading 13. 8 Exercises Embedded options 14. 1 Summary 14. 2 Introduction 14. 3 Guaranteed minimum maturity bene? t 14. 3. 1 Pricing 14. 3. 2 Reserving 14. 4 Guaranteed minimum death bene? t 14. 4. 1 Pricing 14. 4. 2 Reserving 369 369 374 374 374 375 384 388 390 390 391 393 394 395 395 401 401 401 402 403 405 405 405 410 413 414 414 416 427 428 431 431 431 433 433 436 438 438 440 12 13 14 Contents 14. 5 Pricing methods for embedded options 14. 6 Risk solicitude 14. 7 Emerging costs 14. Notes and further reading 14. 9 Exercises A luck theory A. 1 Probability distributions A. 1. 1 Binomial distribution A. 1. 2 Uniform distribution A. 1. 3 Normal distribution A. 1. 4 Lognormal distribution A. 2 The central limit theorem A. 3 Functions of a random variable A. 3. 1 Discrete random variables A. 3. 2 Continuous random variables A. 3. 3 Mixed random variables A. 4 Conditional presentiment and conditional varianc e A. 5 Notes and further reading B Numerical techniques B. 1 Numerical integration B. 1. 1 The trapezium rule B. 1. 2 iterate Simpsons rule B. 1. 3 Integrals over an in? nite interval B. Woolhouses formula B. 3 Notes and further reading C Simulation C. 1 The opposition transform method C. 2 Simulation from a normal distribution C. 2. 1 The BoxMuller method C. 2. 2 The polar method C. 3 Notes and further reading References Author index Index xiii 444 447 449 457 458 464 464 464 464 465 466 469 469 470 470 471 472 473 474 474 474 476 477 478 479 480 480 481 482 482 482 483 487 488 Preface Life insurance has undergone enormous change in the last two to three decades. New and innovative products gain been developed at the same time as we have seen vast increases in computational power.In addition, the ? eld of ? nance has experient a revolution in the development of a mathematical theory of options and ? nancial guarantees, ? rst pioneered in the work of Black, Scholes and Merton, and actuaries have come to realize the importance of that work to risk palmment in actuarial contexts. Given the changes occurring in the interconnected worlds of ? nance and life insurance, we believe that this is a good time to recast the mathematics of life contingent risk to be better adapted to the products, science and technology that are relevant to current and future actuaries.In this book we have developed the theory to measure and manage risks that are contingent on demographic experience as well as on ? nancial variables. The material is presented with a certain take aim of mathematical rigour we intend for readers to understand the principles twisting, rather than to memorize methods or formulae. The reason is that a unyielding approach will prove more utilizable in the long run than a short-term utilitarian outlook, as theory can be adapted to changing products and technology in ways that techniques, without scienti? c support, cannot.We beginning from a traditio nal approach, and then develop a more coetaneous perspective. The ? rst seven chapters set the context for the material, and cover traditional actuarial models and theory of life contingencies, with modern computational techniques integrated by means ofout, and with an emphasis on the practical context for the survival models and valuation methods presented. Through the focus on realistic contracts and assumptions, we aim to foster a general business awareness in the life insurance context, at the same time as we develop the mathematical tools for risk management in that context. iv Preface xv In Chapter 8 we introduce multiple state models, which generalize the life death adventure structure of previous chapters. Using multiple state models al bases a single framework for a wide range of insurance, including bene? ts which depend on health status, on cause of death bene? ts, or on two or more lives. In Chapter 9 we apply the theory developed in the earlier chapters to problems i nvolving pension bene? ts. Pension mathematics has rough specialized c erstpts, particularly in funding principles, but in general this chapter is an application of the theory in the preceding chapters.In Chapter 10 we move to a more sophisticated view of chase rate models and interest rate risk. In this chapter we explore the crucially important difference mingled with diversi? able and non-diversi? able risk. Investment risk represents a source of non-diversi? able risk, and in this chapter we show how we can reduce the risk by matching cash ? ows from assets and liabilities. In Chapter 11 we continue the cash ? ow approach, developing the emerging cash ? ows for traditional insurance products. One of the liberating aspects of the computer revolution for actuaries is that we are no longitudinal craved to summarize complex bene? s in a single actuarial value we can go much further in project the cash ? ows to see how and when surplus will emerge. This is much richer informatio n that the actuary can use to assess pro? tability and to better manage portfolio assets and liabilities. In Chapter 12 we repeat the emerging cash ? ow approach, but here we look at equity-linked contracts, where a ? nancial guarantee is uncouthly part of the contingent bene? t. The real risks for such products can only be assessed taking the random variation in potential outcomes into consideration, and we demonstrate this with Monte Carlo simulation of the emerging cash ? ws. The products that are explored in Chapter 12 contain ? nancial guarantees embedded in the life contingent bene? ts. Option theory is the mathematics of valuation and risk management of ? nancial guarantees. In Chapter 13 we introduce the perfect assumptions and results of option theory. In Chapter 14 we apply option theory to the embedded options of ? nancial guarantees in insurance products. The theory can be apply for pricing and for find appropriate reserves, as well as for assessing pro? tability.Th e material in this book is designed for undergraduate and graduate programmes in actuarial science, and for those self-studying for professional actuarial exams. Students should have suf? cient background in opportunity to be able to calculate moments of functions of one or two random variables, and to handle conditional expectations and variances. We also stomach familiarity with the binomial, uniform, exponential, normal and lognormal distributions. Some of the more important results are reviewed in Appendix A. We also lay claim xvi Preface that readers have completed an introductory direct course in the mathematics of ? ance, and are aware of the actuarial notation for annuities-certain. Throughout, we have opted to use examples that liberally call on spreadsheetstyle software. Spreadsheets are ubiquitous tools in actuarial practice, and it is natural to use them finishedout, allowing us to use more realistic examples, rather than having to simplify for the sake of mathemati cal tractability. Other software could be used equally effectively, but spreadsheets represent a fairly universal language that is easily accessible. To keep the computation requirements reasonable, we have battend hat e really example and exercise can be completed in Microsoft Excel, without needing any VBA code or macros. Readers who have suf? cient familiarity to write their own code whitethorn ? nd more ef? cient solutions than those that we have presented, but our principle was that no reader should need to know more than the basic Excel functions and applications. It will be really useful for anyone working through the material of this book to construct their own spreadsheet tables as they work through the ? rst seven chapters, to generate mortality and actuarial functions for a range of mortality models and interest rates.In the worked examples in the text, we have worked with greater accuracy than we record, so there will be close to differences from rounding when working with modal(a) ? gures. One of the advantages of spreadsheets is the ease of carrying into action of numerical integration algorithms. We assume that students are aware of the principles of numerical integration, and we give some of the most useful algorithms in Appendix B. The material in this book is appropriate for two one-semester courses. The ? rst seven chapters form a fairly traditional rear, and would reasonably constitute a ? st course. Chapters 814 introduce more contemporary material. Chapter 13 whitethorn be omitted by readers who have studied an introductory course covering pricing and delta hedging in a BlackScholesMerton model. Chapter 9, on pension mathematics, is not required for subsequent chapters, and could be omitted if a single focus on life insurance is preferred. Acknowledgements Many of our students and colleagues have made worth(predicate) comments on earlier drafts of parts of the book. Particular thanks go to Carole Bernard, Phelim Boyle, Johnny Li, Ana Maria Mera, Kok Keng Siaw and Matthew Till.The authors gratefully acknowledge the contribution of the Departments of Statistics and Actuarial Science, University of Waterloo, and Actuarial Mathematics and Statistics, Heriot-Watt University, in welcoming the non-resident Preface xvii authors for short visits to work on this book. These visits signi? cantly shortened the time it has taken to write the book (to only one year beyond the original deadline). David Dickson University of Melbourne Mary Hardy University of Waterloo Howard Waters Heriot-Watt University 1 Introduction to life insurance 1. Summary Actuaries apply scienti? c principles and techniques from a range of other disciplines to problems involving risk, misgiving and ? nance. In this chapter we set the context for the mathematics of later chapters, by describing some of the background to modern actuarial practice in life insurance, followed by a brief description of the major types of life insurance products that ar e sold in developed insurance markets. Because pension liabilities are akin(predicate) in some(prenominal) ways to life insurance liabilities, we also describe some common pension bene? ts.We give examples of the actuarial questions arising from the risk management of these contracts. How to answer such questions, and conclude the resulting problems, is the subject of the following chapters. 1. 2 Background The ? rst actuaries were employed by life insurance companies in the early eighteenth century to provide a scienti? c basis for managing the companies assets and liabilities. The liabilities depended on the number of deaths occurring amongst the ensure lives each year. The modelling of mortality became a topic of both commercial and general scienti? interest, and it attracted numerous signi? cant scientists and mathematicians to actuarial problems, with the result that much of the early work in the ? eld of probability was closely connected with the development of solutions to actuarial problems. The earliest life insurance policies provided that the policyholder would pay an amount, called the premium, to the insurer. If the named life insured died during the year that the contract was in force, the insurer would pay a predetermined lump sum, the sum insured, to the policyholder or his or her estate. So, the ? st life insurance contracts were annual contracts. Each year the premium would increase as the probability of death increased. If the insured life became very ill at the renewal date, the insurance ability not be renewed, in which case 1 2 Introduction to life insurance no bene? t would be paying on the lifes subsequent death. Over a large number of contracts, the premium income each year should or so match the claims surmount. This method of matching income and outgo annually, with no attempt to smooth or balance the premiums over the years, is called assessmentism.This method is hush up used for group life insurance, where an employer purc hases life insurance cover for its employees on a year-to-year basis. The radical development in the later eighteenth century was the level premium contract. The problem with assessmentism was that the annual increases in premiums discouraged policyholders from renewing their contracts. The level premium policy offered the policyholder the option to lock-in a regular premium, payable perhaps weekly, monthly, quarterly or annually, for a number of years.This was much more popular with policyholders, as they would not be priced out of the insurance contract just when it might be most needed. For the insurer, the attraction of the longer contract was a greater likeliness of the policyholder paying premiums for a longer period. However, a problem for the insurer was that the longer contracts were more complex to model, and offered more ? nancial risk. For these contracts then, actuarial techniques had to develop beyond the year-to-year modelling of mortality probabilities. In particula r, it became necessary to incorporate ? nancial considerations into the modelling of income and outgo.Over a one-year contract, the time value of money is not a critical aspect. Over, say, a 30-year contract, it becomes a very important part of the modelling and management of risk. another(prenominal) development in life insurance in the nineteenth century was the concept of insurable interest. This was a requirement in law that the person contracting to pay the life insurance premiums should face a ? nancial loss on the death of the insured life that was no less(prenominal) than the sum insured under the policy. The insurable interest requirement disallowed the use of insurance as a form of gambling on the lives of public ? ures, but more importantly, removed the incentive for a policyholder to hasten the death of the named insured life. Subsequently, insurance policies tended to be purchased by the insured life, and in the rest of this book we use the convention that the policyhol der who pays the premiums is also the life insured, whose survival or death triggers the payment of the sum insured under the conditions of the contract. The earliest studies of mortality admit life tables constructed by John Graunt and Edmund Halley. A life table summarizes a survival model by specifying the proportion of lives that are expected to survive to each age.Using London mortality data from the early s government issueeenth century, Graunt proposed, for example, that each new life had a probability of 40% of surviving to age 16, and a probability of 1% of surviving to age 76. Edmund Halley, famous for his astronomical calculations, used mortality data from the city of Breslau in the late seventeenth century as the basis for his life table, which, like Graunts, was constructed by 1. 3 Life insurance and annuity contracts 3 proposing the average (medium in Halleys phrase) proportion of survivors to each age from an arbitrary number of births.Halley took the work two steps further. First, he used the table to draw inference about the conditional survival probabilities at intermediate ages. That is, given the probability that a newborn life survives to each subsequent age, it is possible to infer the probability that a life aged, say, 20, will survive to each subsequent age, using the condition that a life aged zero survives to age 20. The second major innovation was that Halley merged the mortality data with an assumption about interest rates to ? nd the value of a social unit life annuity at different ages.A whole life annuity is a contract paying a level sum at regular intervals while the named life (the annuitant) is still alive. The calculations in Halleys paper bear a remarkable similarity to some of the work still used by actuaries in pensions and life insurance. This book continues in the tradition of combining models of mortality with models in ? nance to develop a framework for pricing and risk management of long-term policies in life insur ance. Many of the same techniques are relevant also in pensions mathematics. However, there have been many changes since the ? st long-term policies of the late eighteenth century. 1. 3 Life insurance and annuity contracts 1. 3. 1 Introduction The life insurance and annuity contracts that were the object of study of the early actuaries were very similar to the contracts written up to the 1980s in all the developed insurance markets. Recently, however, the design of life insurance products has radically changed, and the techniques needed to manage these more modern contracts are more complex than ever. The reasons for the changes intromit Increased interest by the insurers in oblation combined nest egg and insurance products. The original life insurance products offered a payment to indemnify (or offset) the hardship caused by the death of the policyholder. Many modern contracts combine the indemnity concept with an opportunity to invest. More powerful computational facilities allow more complex products to be modelled. Policyholders have become more sophisticated investors, and require more options in their contracts, allowing them to vary premiums or sums insured, for example. More competition has led to insurers creating increasingly complex products in order to attract more business.The risk management techniques in ? nancial products have also become increasingly complex, and insurers have offered some bene? ts, particularly 4 Introduction to life insurance ? nancial guarantees, that require sophisticated techniques from ? nancial engine room to measure and manage the risk. In the remainder of this section we describe some of the most important modern insurance contracts, which will later be used as examples in the book. Different countries have different names and types of contracts we have tried to cover the major contract types in wedlock America, the United solid ground and Australia.The basic transaction of life insurance is an exchange the policyholder pays premiums in return for a later payment from the insurer which is life contingent, by which we mean that it depends on the death or survival or possibly the state of health of the policyholder. We usually use the term insurance when the bene? t is paid as a single lump sum, each on the death of the policyholder or on survival to a predetermined maturity date. (In the UK it is common to use the term assurance for insurance contracts involving lives, and insurance for contracts involving prop. ) An annuity is a bene? in the form of a regular series of payments, usually conditional on the survival of the policyholder. 1. 3. 2 Traditional insurance contracts Term, whole life and endowment insurance are the traditional products, providing cash bene? ts on death or maturity, usually with predetermined premium and bene? t amounts. We describe each in a little more detail here. Term insurance pays a lump sum bene? t on the death of the policyholder, provided death occurs before the end of a speci? ed term. Term insurance allows a policyholder to provide a ? xed sum for his or her dependents in the event of the policyholders death.Level term insurance contends a level sum insured and regular, level premiums. Decreasing term insurance indicates that the sum insured and (usually) premiums decrease over the term of the contract. Decreasing term insurance is popular in the UK where it is used in conjunction with a home mortgage if the policyholder dies, the remaining mortgage is paid from the term insurance proceeds. Renewable term insurance offers the policyholder the option of renewing the policy at the end of the original term, without further evidence of the policyholders health status.In North America, Yearly Renewable Term (YRT) insurance is common, under which insurability is guaranteed for some ? xed period, though the contract is written only for one year at a time. 1. 3 Life insurance and annuity contracts 5 Convertible term insurance offers the policyholder the option to convert to a whole life or endowment insurance at the end of the original term, without further evidence of the policyholders health status. Whole life insurance pays a lump sum bene? t on the death of the policyholder whenever it occurs.For regular premium contracts, the premium is often payable only up to some maximum age, such as 80. This avoids the problem that older lives may be less able to pay the premiums. Endowment insurance offers a lump sum bene? t paid either on the death of the policyholder or at the end of a speci? ed term, whichever occurs ? rst. This is a mixture of a term insurance bene? t and a savings element. If the policyholder dies, the sum insured is paid just as under term insurance if the policyholder survives, the sum insured is treated as a maturing enthronization. Endowment insurance is obsolete in many jurisdictions.Traditional endowment insurance policies are not currently sold in the UK, but there are large portfolios of policies on the books of UK insurers, because until the late 1990s, endowment insurance policies were often used to repay home mortgages. The policyholder (who is the home owner) paid interest on the mortgage loan, and the principal was paid from the proceeds on the endowment insurance, either on the death of the policyholder or at the ? nal mortgage repayment date. Endowment insurance policies are becoming popular in developing nations, particularly for micro-insurance where the amounts involved are small.It is hard for small investors to achieve good rates of return on investments, because of heavy expense charges. By pooling the death and survival bene? ts under the endowment contract, the policyholder gains on the investment side from the resulting economies of scale, and from the investment expertise of the insurer. With-pro? t insurance Also part of the traditional design of insurance is the division of business into with-pro? t (also known, especially in North America, as pa rticipating, or par business), and without pro? t (also known as non-participating or non-par). Under with-pro? t arrangements, the pro? s earned on the invested premiums are shared with the policyholders. In North America, the with-pro? t arrangement often takes the form of cash dividends or reduced premiums. In the UK and in Australia the traditional approach is to use the pro? ts to increase the sum insured, through bonuses called reversionary bonusesand endpoint bonuses. Reversionary bonuses are awarded during the term of the contract once a reversionary bonus is awarded it is guaranteed. Terminal bonuses are awarded when the policy matures, either through the death of the insured, or when an endowment policy reaches the end of the term.Reversionary bonuses 6 Introduction to life insurance Table 1. 1. Year 1 2 3 . . . Bonus on original sum insured 2% 2. 5% 2. 5% . . . Bonus on bonus 5% 6% 6% . . . Total bonus 2000. 00 4620. 00 7397. 20 . . . may be expressed as a per centum of the total of the previous sum insured plus bonus, or as a percentage of the original sum insured plus a different percentage of the previously declared bonuses. Reversionary and terminal bonuses are determined by the insurer based on the investment performance of the invested premiums. For example, suppose an insurance is issued with sum insured $100 000.At the end of the ? rst year of the contract a bonus of 2% on the sum insured and 5% on previous bonuses is declared in the following two years, the rates are 2. 5% and 6%. accordingly the total guaranteed sum insured increases each year as shown in Table 1. 1. If the policyholder dies, the total death bene? t payable would be the original sum insured plus reversionary bonuses already declared, increased by a terminal bonus if the investment returns earned on the premiums have been suf? cient. With-pro? ts contracts may be used to offer policyholders a savings element with their life insurance.However, the traditional with-pro? t contract is designed primarily for the life insurance cover, with the savings aspect a secondary feature. 1. 3. 3 Modern insurance contracts In recent years insurers have provided more ? exible products that combine the death bene? t coverage with a signi? cant investment element, as a way of competing for policyholderssavings with other institutions, for example, banks or open-ended investment companies (e. g. reciprocal funds in North America, or unit trusts in the UK). Additional ?exibility also allows policyholders to purchase less insurance when their ? ances are tight, and then increase the insurance coverage when they have more money available. In this section we describe some examples of modern, ? exible insurance contracts. normal life insurance combines investment and life insurance. The policyholder determines a premium and a level of life insurance cover. Some 1. 3 Life insurance and annuity contracts 7 of the premium is used to fund the life insurance the remainder is paid into an investment fund. Premiums are ? exible, as long as they are suf? cient to pay for the designated sum insured under the term insurance part of the contract.Under variable universal life, there is a range of funds available for the policyholder to select from. oecumenical life is a common insurance contract in North America. Unitized with-pro? t is a UK insurance contract it is an evolution from the conventional with-pro? t policy, designed to be more transparent than the original. Premiums are used to purchase units (shares) of an investment fund, called the with-pro? t fund. As the fund earns investment return, the shares increase in value (or more shares are issued), increasing the bene? t entitlement as reversionary bonus.The shares will not decrease in value. On death or maturity, a further terminal bonus may be payable depending on the performance of the with-pro? t fund. After some poor publicity surrounding with-pro? t business, and, by association, unitized wit h-pro? t business, these product designs were withdrawn from the UK and Australian markets by the early 2000s. However, they will remain important for many years as many companies carry very large portfolios of with-pro? t (traditional and unitized) policies issued during the second half of the twentieth century.Equity-linked insurance has a bene? t linked to the performance of an investment fund. There are two different forms. The ? rst is where the policyholders premiums are invested in an open-ended investment company style account at maturity, the bene? t is the accumulated value of the premiums. There is a guaranteed minimum death bene? t payable if the policyholder dies before the contract matures. In some cases, there is also a guaranteed minimum maturity bene? t payable. In the UK and most of Europe, these are called unit-linked policies, and they rarely carry a guaranteed maturity bene? . In Canada they are known as segregated fund policies and always carry a maturity guara ntee. In the USA these contracts are called variable annuity contracts maturity guarantees are increasingly common for these policies. (The use of the term annuity for these contracts is very misleading. The bene? ts are designed with a single lump sum payout, though there may be an option to convert the lump sum to an annuity. ) The second form of equity-linked insurance is the Equity-Indexed rente (EIA) in the USA.Under an EIA the policyholder is guaranteed a minimum return on their premium (minus an initial expense charge). At maturity, the policyholder take ons a proportion of the return on a speci? ed stock index, if that is greater than the guaranteed minimum return. EIAs are chiefly rather shorter in term than unit-linked products, with seven-year policies being typical variable annuity contracts commonly 8 Introduction to life insurance have terms of twenty years or more. EIAs are much less popular with consumers than variable annuities. 1. 3. 4 Distribution methods clos e to people ? d insurance dauntingly complex. Brokers who connect individuals to an appropriate insurance product have, since the earliest times, played an important role in the market. There is an old saying amongst actuaries that insurance is sold, not bought, which means that the role of an intermediary in persuading potential policyholders to take out an insurance policy is crucial in maintaining an up to(predicate) volume of new business. Brokers, or other ? nancial advisors, are often remunerated through a commission system. The commission would be speci? ed as a percentage of the premium paid.Typically, there is a higher percentage paid on the ? rst premium than on subsequent premiums. This is referred to as a front-end load. Some advisors may be remunerated on a ? xed fee basis, or may be employed by one or more insurance companies on a wages basis. An alternative to the broker method of selling insurance is direct marketing. Insurers may use television advertising or othe r telemarketing methods to sell direct to the public. The nature of the business sold by direct marketing methods tends to differ from the broker sold business. For example, often the sum insured is smaller.The policy may be aimed at a niche market, such as older lives concerned with insurance to cover their own funeral expenses (called pre-need insurance in the USA). Another mass marketed insurance contract is loan or credit insurance, where an insurer might cover loan or credit card payments in the event of the borrowers death, disability or unemployment. 1. 3. 5 Underwriting It is important in modelling life insurance liabilities to consider what happens when a life insurance policy is purchased. interchange life insurance policies is a competitive business and life insurance companies (also known as life of? es) are constantly considering ways in which to change their procedures so that they can improve the service to their customers and gain a commercial advantage over their competitors. The account given below of how policies are sold covers some essential points but is necessarily a simpli? ed version of what actually happens. For a given type of policy, say a 10-year term insurance, the life of? ce will have a schedule of premium rates. These rates will depend on the size of the policy and some other factors known as rating factors.An appliers risk level is assessed by asking them to complete a proposal form giving information on 1. 3 Life insurance and annuity contracts 9 relevant rating factors, generally including their age, gender, smoking habits, occupation, any dangerous hobbies, and personal and family health history. The life insurer may ask for permission to contact the applicants doctor to enquire about their medical history. In some cases, particularly for very large sums insured, the life insurer may require that the applicants health be checked by a doctor employed by the insurer.The process of pile up and evaluating this information i s called underwriting. The purpose of underwriting is, ? rst, to classify potential policyholders into broadly homogeneous risk categories, and secondly to assess what additional premium would be appropriate for applicants whose risk factors indicate that standard premium rates would be too low. On the basis of the application and supporting medical information, potential life insurance policyholders will generally be categorized into one of the following groups Preferred lives have very low mortality risk based on the standard infor- mation.The preferred applicant would have no recent record of smoking no evidence of drug or alcohol abuse no high-risk hobbies or occupations no family history of disease known to have a strong genetic component no adverse medical indicators such as high root pressure or cholesterol level or body mass index. The preferred life category is common in North America, but has not yet caught on elsewhere. In other areas there is no separation of preferred and normal lives. Normal lives may have some higher rated risk factors than preferred lives (where this category exists), but are still insurable at standard rates.Most applicants fall into this category. Rated lives have one or more risk factors at raised levels and so are not acceptable at standard premium rates. However, they can be insured for a higher premium. An example might be someone having a family history of heart disease. These lives might be individually assessed for the appropriate additional premium to be charged. This category would also include lives with hazardous jobs or hobbies which put them at increased risk. Uninsurable lives have such signi? ant risk that the insurer will not enter an insurance contract at any price. Within the ? rst three groups, applicants would be further categorized according to the relative values of the various risk factors, with the most cardinal being age, gender and smoking status. Most applicants (around 95% for traditional lif e insurance) will be accepted at preferred or standard rates for the relevant risk category. Another 23% may be accepted at non-standard rates 10 Introduction to life insurance because of an impairment, or a dangerous occupation, leaving around 23% who ill be refused insurance. The rigour of the underwriting process will depend on the type of insurance being purchased, on the sum insured and on the distribution process of the insurance company. Term insurance is generally more strictly underwritten than whole life insurance, as the risk taken by the insurer is greater. Under whole life insurance, the payment of the sum insured is certain, the uncertainty is in the timing. Under, say, 10-year term insurance, it is faux that the majority of contracts will expire with no death bene? t paid.If the underwriting is not strict there is a risk of adverse selection by policyholders that is, that very high-risk individuals will buy insurance in disproportionate numbers, leading to excessive losses. Since high sum insured contracts carry more risk than low sum insured, high sums insured would generally trigger more rigorous underwriting. The marketing method also affects the level of underwriting. Often, direct marketed contracts are sold with relatively low bene? t levels, and with the attraction that no medical evidence will be sought beyond a standard questionnaire.The insurer may assume relatively heavy mortality for these lives to compensate for potential adverse selection. By keeping the underwriting relatively light, the expenses of writing new business can be unplowed low, which is an attraction for high-volume, low sum insured contracts. It is interesting to note that with no third party medical evidence the insurer is placing a lot of tip on the veracity of the policyholder. Insurers have a phrase for this that both insurer and policyholder may assume utmost good faith or uberrima ? es on the part of the other side of the contract. In practice, in the even t of the death of the insured life, the insurer may investigate whether any pertinent information was withheld from the application. If it appears that the policyholder held back information, or submitted false or misleading information, the insurer may not pay the full sum insured. 1. 3. 6 Premiums A life insurance policy may involve a single premium, payable at the outset of the contract, or a regular series of premiums payable provided the policyholder survives, perhaps with a ? ed end date. In traditional contracts the regular premium is generally a level amount throughout the term of the contract in more modern contracts the premium might be variable, at the policyholders discretion for investment products such as equity-linked insurance, or at the insurers discretion for certain types of term insurance. Regular premiums may be paid annually, semi-annually, quarterly, monthly or weekly. Monthly premiums are common as it is convenient for policyholders to have their outgoings pa yable with approximately the same frequency as their income. . 3 Life insurance and annuity contracts 11 An important feature of all premiums is that they are paid at the deviate of each period. Suppose a policyholder contracts to pay annual premiums for a 10-year insurance contract. The premiums will be paid at the start of the contract, and then at the start of each subsequent year provided the policyholder is alive. So, if we count time in years from t = 0 at the start of the contract, the ? rst premium is paid at t = 0, the second is paid at t = 1, and so on, to the tenth premium paid at t = 9.Similarly, if the premiums are monthly, then the ? rst monthly instalment will be paid at t = 0, and the ? nal premium will be paid at the start 11 of the ? nal month at t = 9 12 years. (Throughout this book we assume that all 1 months are equal in length, at 12 years. ) 1. 3. 7 Life annuities Annuity contracts offer a regular series of payments. When an annuity depends on the survival of the recipient, it is called a life annuity. The recipient is called an annuitant. If the annuity continues until the death of the annuitant, it is called a whole life annuity.If the annuity is paid for some maximum period, provided the annuitant survives that period, it is called a term life annuity. Annuities are often purchased by older lives to provide income in solitude. Buying a whole life annuity guarantees that the income will not run out before the annuitant dies. Single Premium Deferred Annuity (SPDA) Under an SPDA contract, the policyholder pays a single premium in return for an annuity which commences payment at some future, speci? ed date. The annuity is life contingent, by which we mean the annuity is paid only if the policyholder survives to the payment dates.If the policyholder dies before the annuity commences, there may be a death bene? t due. If the policyholder dies soon after the annuity commences, there may be some minimum payment period, called the guarantee period, and the balance would be paid to the policyholders estate. Single Premium Immediate Annuity (SPIA) This contract is the same as the SPDA, get out that the annuity commences as soon as the contract is effected. This might, for example, be used to convert a lump sum retirement bene? t into a life annuity to supplement a pension.As with the SPDA, there may be a guarantee period applying in the event of the early death of the annuitant. Regular Premium Deferred Annuity (RPDA) The RPDA offers a deferred life annuity with premiums paid through the deferred period. It is otherwise the same as the SPDA. Joint life annuity A joint life annuity is issued on two lives, typically a married couple. The annuity (which may be single premium or regular 12 Introduction to life insurance premium, immediate or deferred) continues while both lives survive, and ceases on the ? rst death of the couple.Last survivor annuity A last survivor annuity is similar to the joint life annuity, except that payment continues while at least one of the lives survives, and ceases on the second death of the couple. Reversionary annuity A reversionary annuity is contingent on two lives, usually a couple. One is designated as the annuitant, and one the insured. No annuity bene? t is paid while the insured life survives. On the death of the insured life, if the annuitant is still alive, the annuitant receives an annuity for the remainder of his or her life. 1. Other insurance contracts The insurance and annuity contracts described above are all contingent on death or survival. There are other life contingent risks, in particular involving shortterm or long-term disability. These are known as morbidity risks. Income protection insurance When a person becomes sick and cannot work, their income will, eventually, be affected. For someone in regular employment, the employer may cover salary for a period, but if the indisposition continues the salary will be decreased, and ultimately will stop be ing paid at all. For someone who is elf-employed, the effects of sickness on income will be immediate. Income protection policies replace at least some income during periods of sickness. They usually cease at retirement age. Critical illness insurance Some serious illnesses can cause signi? cant expense at the onset of the illness. The patient may have to leave employment, or alter their home, or incur severe medical expenses. Critical illness insurance pays a bene? t on diagnosis of one of a number of severe conditions, such as certain cancers or heart disease. The bene? t is usually in the form of a lump sum.Long-term bang insurance This is purchased to cover the costs of care in old age, when the insured life is unable to continue living independently. The bene? t would be in the form of the long-term care costs, so is an annuity bene? t. 1. 5 Pension bene? ts Many actuaries work in the area of pension plan design, valuation and risk management. The pension plan is usually spons ored by an employer. Pension plans typically offer employees (also called pension plan members) either lump 1. 5 Pension bene? ts 13 sums or annuity bene? ts or both on retirement, or deferred lump sum or annuity bene? s (or both) on earlier withdrawal. Some offer a lump sum bene? t if the employee dies while still employed. The bene? ts therefore depend on the survival and employment status of the member, and are quite similar in nature to life insurance bene? ts that is, they involve investment of contributions long into the future to pay for future life contingent bene? ts. 1. 5. 1 De? ned bene? t and de? ned contribution pensions De? ned Bene? t (DB) pensions offer retirement income based on service and salary with an employer, using a de? ned formula to determine the pension.For example, suppose an employee reaches retirement age with n years of service (i. e. membership of the pension plan), and with pensionable salary averaging S in, say, the ? nal three years of employment. A typical ? nal salary plan might offer an annual pension at retirement of B = Sn? , where ? is called the accrual rate, and is usually around 1%2%. The formula may be interpreted as a pension bene? t of, say, 2% of the ? nal average salary for each year of service. The de? ned bene? t is funded by contributions paid by the employer and (usually) the employee over the working lifetime of the employee.The contributions are invested, and the accumulated contributions must be enough, on average, to pay the pensions when they become due. De? ned Contribution (DC) pensions work more like a bank account. The employee and employer pay a predetermined contribution (usually a ? xed percentage of salary) into a fund, and the fund earns interest. When the employee leaves or retires, the proceeds are available to provide income throughout retirement. In the UK most of the proceeds must be converted to an annuity.In the USA and Canada there are more options the pensioner may draw funds to live on without necessarily purchasing an annuity from an insurance company. 1. 5. 2 De? ned bene? t pension design The age retirement pension described in the section above de? nes the pension payable from retirement in a standard ? nal salary plan. Career average salary plans are also common in some jurisdictions, where the bene? t formula is the same as the ? nal salary formula above, except that the average salary over the employees entire career is used in place of the ? nal salary. Many employees leave their jobs before they retire.A typical withdrawal bene? t would be a pension based on the same formula as the age retirement bene? t, but with the start date deferred until the employee reaches the normal retirement age. Employees may have the option of taking a lump sum with the 14 Introduction to life insurance same value as the deferred pension, which can be invested in the pension plan of the new employer. Some pension plans also offer death-in-service bene? ts, for employees w ho die during their period of employment. Such bene? ts might include a lump sum, often based on salary and sometimes service, as well as a pension for the employees spouse. . 6 Mutual and proprietary insurers A mutual insurance company is one that has no shareholders. The insurer is owned by the with-pro? t policyholders. All pro? ts are distributed to the with-pro? t policyholders through dividends or bonuses. A proprietary insurance company has shareholders, and usually has withpro? t policyholders as well. The participating policyholders are not owners, but have a speci? ed right to some of the pro? ts. Thus, in a proprietary insurer, the pro? ts must be shared in some predetermined proportion, between the shareholders and the with-pro? t policyholders.Many early life insurance companies were formed as mutual companies. More recently, in the UK, Canada and the USA, there has been a trend towards demutualization, which means the transition of a mutual company to a proprietary com pany, through issuing shares (or cash) to the with-pro? t policyholders. Although it would appear that a mutual insurer would have marketing advantages, as participating policyholders receive all the pro? ts and other bene? ts of ownership, the advantages cited by companies who have demutualized include increased ability to raise capital, clearer corporate structure and improved ef? iency. 1. 7 Typical problems We are concerned in this book with developing the mathematical models and techniques used by actuaries working in life insurance and pensions. The primary responsibility of the life insurance actuary is to maintain the solvency and pro? tability of the insurer. Premiums must be suf? cient to pay bene? ts the assets held must be suf? cient to pay the contingent liabilities bonuses to policyholders should be fair. Consider, for example, a whole life insurance contract issued to a life aged 50. The sum insured may not be paid for 30 years or more.The premiums paid over the perio d will be invested by the insurer to earn signi? cant interest the accumulated premiums must be suf? cient to pay the bene? ts, on average. To ensure this, the actuary needs to model the survival probabilities of the policyholder, the investment returns likely to be earned and the expenses likely 1. 9 Exercises 15 to be incurred in maintaining the policy. The actuary may take into consideration the probability that the policyholder decides to terminate the contract early. The actuary may also consider the pro? tability requirements for the contract.Then, when all of these factors have been modelled, they must be combined to set a premium. Each year or so, the actuary must determine how much money the insurer or pension plan should hold to ensure that future liabilities will be covered with adequately high probability. This is called the valuation process. For with-pro? t insurance, the actuary must determine a suitable level of bonus. The problems are rather more complex if the insu rance also covers morbidity risk, or involves several lives. All of these topics are covered in the following chapters.The actuary may also be involved in decisions about how the premiums are invested. It is vitally important that the insurer remains solvent, as the contracts are very long-term and insurers are responsible for protecting the ? nancial security of the general public. The way the underlying investments are selected can increase or mitigate the risk of insolvency. The precise selection of investments to manage the risk is particularly important where the contracts involve ? nancial guarantees. The pensions actuary working with de? ned bene? t pensions must determine appropriate contribution rates to meet the bene? s promised, using models that allow for the working patterns of the employees. Sometimes, the employer may want to change the bene? t structure, and the actuary is responsible for assessing the cost and impact. When one company with a pension plan takes over another, the actuary must assist with determining the best way to allocate the assets from the two plans, and perhaps how to merge the bene? ts. 1. 8 Notes and further reading A number of essays describing actuarial practice can be found in Renn (ed. ) (1998). This book also provides both historical and more contemporary contexts for life contingencies.The original paper of Graunt and Halley are available online (and any search engine will ? nd them). Anyone interested in the history of probability and actuarial science will ? nd these interesting, and remarkably modern. 1. 9 Exercises Exercise 1. 1 Why do insurers generally require evidence of health from a person applying for life insurance but not for an annuity? 16 Introduction to life insurance Exercise 1. 2 Explain wherefore an insurer might demand more rigorous evidence of a prospective policyholders health status for a term insurance than for a whole life insurance. Exercise 1. Explain why premiums are payable in advance, so that the ? rst premium is due now rather than in one years time. Exercise 1. 4 Lenders religious offering mortgages to home owners may require the borrower to purchase life insurance to cover the outstanding loan on the death of the borrower, even though the mortgaged property is the loan collateral. (a) Explain why the lender might require term insurance in this circumstance. (b) Describe how this term insurance might differ from the standard term insurance described in Section 1. 3. 2. (c) Can you see any problems with lenders demanding term insurance from borrowers?Exercise 1. 5 Describe the difference between a cash bonus and a reversionary bonus for with-pro? t whole life insurance. What are the advantages and disadvantages of each for (a) the insurer and (b) the policyholder? Exercise 1. 6 It is common for insurers to design whole life contracts with premiums payable only up to age 80. Why? Exercise 1. 7 Andrew is retired. He has no pension, but has capital of $ viosterol 000. He is considering the following options for using the money (a) leveraging an annuity from an insurance company that will pay a level amount for the rest of his life. b) Purchase an annuity from an insurance company that will pay an amount that increases with the cost of living for the rest of his life. (c) Purchase a 20-year annuity certain. (d) Invest the capital and live on the interest income. (e) Invest the capital and draw $40 000 per year to live on. What are the advantages and disadvantages of each option? 2 Survival models 2. 1 Summary In this chapter we represent the future lifetime of an individual as a random variable, and show how probabilities of death or survival can be figure under this framework.We then de? ne an important quantity known as the force of mortality, introduce some actuarial notation, and discuss some properties of the distribution of future lifetime. We introduce the curtate future lifetime random variable. This is a function of the future life time random variable which represents the number of complete years of future life. We excuse why this function is useful and derive its probability function. 2. 2 The future lifetime random variable In Chapter 1 we saw that many insurance policies provide a bene? t on the death of the policyholder.When an insurance company issues such a policy, the policyholders date of death is unknown, so the insurer does not know exactly when the death bene? t will be payable. In order to estimate the time at which a death bene? t is payable, the insurer needs a model of human mortality, from which probabilities of death at particular ages can be calculated, and this is the topic of this chapter. We start with some notation. Let (x) denote a life aged x, where x ? 0. The death of (x) can occur at any age greater than x, and we model the future lifetime of (x) by a continuous random variable which we denote by Tx .This means that x + Tx represents the age-at-death random variable for (x). Let Fx b e the distribution function of Tx , so that Fx (t) = PrTx ? t. Then Fx (t) represents the probability that (x) does not survive beyond age x + t, and we refer to Fx as the lifetime distribution from age x. In many life 17 18 Survival models insurance problems we are interested in the probability of survival rather than death, and so we de? ne Sx as Sx (t) = 1 ? Fx (t) = PrTx t. Thus, Sx (t) represents the probability that (x) survives for at least t years, and Sx is known as the survival function. Given our interpretation of the ollection of random variables Tx x? 0 as the future lifetimes of individuals, we need a federation between any pair of them. To see this, consider T0 and Tx for a particular individual who is now aged