The poem Remember Essay Example for Free

The poem Remember Essay Look again at the poem Remember which is about death and relationships, also look at the poem Remberance which is of similar themes. Look closely at the way the authors have used imagery and structure. Compare and contrast how each feels about death and their relationships. Which poem makes a more powerful appeal to your emotions? Give reasons for your answer. Each of the poems Remember and Remembrance have the similar themes; death and relationships. Remember tell us of a story of a female who is in an impossible relationship that is so bad that she seems to think that her only escape is suicide. She writes to her partner telling him not to grieve for her. The line Better by far you should forget and smile Than that you should remember and be sad. Shows us that she, in a way, doesnt want her partner to be sad. This is kind of hypocritical of this poem. She tells us that she doesnt have another choice to get out of this bad relationship and yet she doesnt want him to suffer. She is obviously a very kind person which makes me feel all the more emotive towards her. Remembrance is telling us a story of a girl who has lost a very dear person to death and we find her pondering suicide herself. This narrator has dug herself a hole in that thinking that she has no point in life anymore without the loved one. She must feel that she cannot go on without said person. Like many people who lose someone dear, she has lost her sense of enthusiasm for life so she, like the narrator in Remember, sees suicide as an escape from a life without a certain person. I can feel her pain, being a person who has lost someone dear to me, I went through a stage of my life where I didnt want to do anything. I didnt even want to go outside. But I am just glad that it did not get to the point where I considered suicide. When writing these poems each woman must have had to dig deep down into their feelings to create such emotive poems. Christina Rossettis father died in 1854, this could have been a very big inspiration for her to bring up so many emotions when writing such a poem. Emily Brontà ¯Ã‚ ¿Ã‚ ½ Also lost her mother which is a very good source of emotions to write with. Each writer has had some experience with death which might be the reason why the only thing they can see as a solution is death itself. They might choose to follow their parents and die. Christina Rossetti uses images such as the silent land which suggests an empty after life where as Emily Brontà ¯Ã‚ ¿Ã‚ ½ uses images such as days of golden dreams which refers to memories that were very dear to her and reminds us that those memories were lost when her loved one died. Each author was very descriptive in their imagery and it was very effective in each poem The layout of Remembrance is much easier to understand than the sonnet structure of the other one. A poem being in stanzas makes it much easier for the reader to read and work out the story behind the poem. I found it much harder to understand Remember as it was in sonnet form (14 lines). A poem being all squashed together makes it had to differentiate one line from the other. My personal preference between these to poems for the one than appeals to me in the emotive way would have to be Remembrance as I can relate to the kind of pain the narrator is going through. The writer has used such emotive language and really made the effort to connect with her own feelings which is a very hard thing to do. And to write them down and make them make sense is a type of magic in itself. A poet is, before anything else, a person who is passionately in love with language. Poetry is language at its most distilled and most powerful and this poet understands that and has somehow tapped into her own language and written her very thoughts down. So on that note I conclude that Remembrance makes the most powerful appeal to my emotions.

Description And Examples Of Genetically Modified Organisms

Description And Examples Of Genetically Modified Organisms Genetically modified organism (GMO), organism whose genome has been engineered in the laboratory in order to favour the expression of desired physiological traits or the production of desired biological products. GMO has long been the practice to breed select individuals of a species to produce offspring of the desirable traits. It is used in conventional livestock production, crop farming and even pet breeding. In genetic modification, the mechanism used for creating a genetically modified organism is called the recombinant DNA technique. It involves combining strands of DNA from different sources to create a new DNA molecule that has a different combination of genes than that, which occurs naturally. There are some scientific methods included in producing GMOs, such as recombinant DNA technology and reproductive cloning. Recombinant DNA technology involves the insertion of one or more individual genes from an organism of one species into the DNA (deoxyribonucleic acid) of another. On the other hand, reproductive cloning technology generates offspring that are genetically identical to the parent by the transfer of an entire donor nucleus into the enucleated cytoplasm of a host egg. The first animal produced using this cloning technique was a sheep named Dolly, born in 1996. Since then a number of other animals, including pigs, horses, and dogs, have been generated using reproductive cloning technology. Cisgenic organisms and transgenic organisms are the two classes of genetically modified organisms. Cisgenic organisms are genetically modified organisms that result from the combination of different strands of DNA, which all originates from the same, or very similar, species. The entire DNA used in the process comes from organisms that are very closely related, usually defined as organisms that are able to breed together. Transgenic organisms are genetically modified organisms that include DNA from two different species. Transgenic microorganisms are the most commonly created transgenic organisms. The simple DNA of bacteria lends itself to relatively straightforward recombinant DNA methods. GMOs produced through genetic technologies are playing a very important role in agriculture, medicine, research, and environmental management. Although GMOs have benefited human society, some disadvantages exist. Therefore, the production of GMOs remains a highly controversial topic in some countries. 2. Examples of Genetically Modified Organisms (GMOs) Many of our common crops, such as corn, potatoes, tomatoes, squash, and soybeans, are genetically modified. The majority of these crops were herbicide-resistant as well as insect-resistant, while the others may contain increased nutrients such as vitamins, produce yield earlier, or are able to survive weather extremes. Genetically modified tomatoes were introduced to the market in 1994, becoming the first commercially grown transgenic crop. They have longer shelf-life than the average tomatoes as they produces less of the substance that causes tomatoes to rot, so remains firm and fresh for a long time. In addition, transgenic corn is resistant to commercial herbicides such as glyphosate or glufosinate. It is also insect resistance by producing a poison, which kills harmful insects. Vitamin-enriched corn contains increased amount of vitamin A, vitamin C and folate compared to the normal corn. Another example of GMO is squash. Squash belongs to the Cucurbitaceae family, which includes pumpkins, gourds, zucchini, cucumbers and melons. Genetically modified squash have resistance to the common squash viruses, namely watermelon mosaic virus, zucchini yellow mosaic virus and cucumber mosaic virus. Other than crops, farm animals are also genetically modified to mature in a shorter time period to minimize expenses and increase profits for farmers, as well as to be resistant to certain diseases. For example, genetically modified cow is resistant to bovine spongiform encephalopathy (mad cow disease). One of the examples of increased growth rate in genetically modified animals is fish including salmon and carp. One-year-old salmon fish with growth hormone chimeric gene are able to grow as large as 13 times that of the non-transgenic salmons. Other than that, chicken that can produce eggs containing human proteins has been created by British by transferring DNA into the yolk of a fertilized chicken embryo. The proteins can be harvested and purified for treatment of diseases such as multiple sclerosis or cancer. 3. Advantages of Genetically Modified Organisms (GMOs) In order to ensure an adequate food supply for this booming population is going to be a major challenge in the years to come. GMO can meet this demand due to its special characteristics. Firstly, GMOs are pest resistance. Pests can cause large financial loss to the farmer. Pesticides that generally used by farmers are health hazarding and causes pollution. Pest resistance can reduce the use of pesticides. Thus, GMOs is healthier to eat and bring less pollution to the environment. Second, GMOs are herbicide and disease resistance. The control of weeds actually is not cost-effective because farmers have to spray large amount of herbicides on the weeds and care has to be taken to avoid the herbicides from harming the crops. Hence, GMOs are more cost-effective and easier to control the weeds and less concern is needed to cope with the diseases caused by viruses, fungi and bacteria. Thirdly, GMOs are drought tolerance/salinity tolerance. As the world population grows and more land is utilized for housing instead of food production, farmers will need to grow crops in locations previously unsuited for plant cultivation. Creating plants that can withstand long periods of drought or high salt content in soil and groundwater will help people to grow crops in formerly less arable places. Next, GMOs have better nutritional value. GMOs are incorporated with other additional vitamins and minerals. For example, blindness due to vitamin A deficiency is a common problem in third world countries. Researchers at the Swiss Federal Institute of Technology Institute for Plant Sciences have created a strain of golden rice containing an unusually high content of beta-carotene (vitamin A). Lastly, GMOs are also useful in pharmaceutical field. Medicines and vaccines often are costly to produce and sometimes require special storage conditions not readily available in third world countries. Researchers are working to develop edible vaccines in tomatoes and potatoes. These vaccines will be much easier to ship, store and administer than traditional injectable vaccines. 4. Criticism Against Genetically Modified Organisms (GMOs) There are several concerns that arise despite the advantages of GMO. The three fields of concern include environmental hazards, human health risks, and economic concerns. One of the environmental hazards consists of gene transfer to non-targeted species. There is a possibility of genetically modified plants cross breeding with weeds to produce weeds to produce a new genetic strain of weeds known as Superweeds. Next concern is the reduced effectiveness of pesticides. The pesticides strains from GMO might be able to pass on to pest after consuming GMO; thus, causing pest to have the same resistant genes to pesticides. These pests are then termed Superpest. The human health risks also posed a major concern among people. The long-term side effects after consuming GMO are still unknown. There is still the question of whether the genetically modified strains are able to pass on to humans after consuming GMO. People are getting worried that the anti-bacterial strain in the GMO might be passed on to humans and cause a disruption in our immunity against certain types of bacteria. There is a possibility that introducing a new gene may create a new allergen or cause an allergic reaction in prone individuals. In addition, there are also economic concerns involved. The cost involved in research and developing of GMOs are high. Many of these GMOs have been patented. Farmers from the third world countries are worried that the price of the patented GMOs would be raised so high that they would not be able to afford it. Furthermore, patent violation has been a growing concern to agribusinesses. Some companies have introduced suicide gene into plants. Suicide gene only allows plants to be viable for one season and the seeds produced after are sterile. Therefore, farmers have to buy fresh seeds every season and this causes an issue to the farmers from the third world countries. 5. Genetically Modified Organisms (GMOs) in Malaysia Malaysia is among the 55 nations in favour of adopting international guidelines on labeling of all genetically modified food. Several genetically modified crops containing traits of value have been produced at the experimental stage. At the Malaysia Agricultural Research and Development institute, rice has been successfully modified to resist the Tungro virus and papayas manipulated to resist ring-spot virus infection and to have a prolonged shelf life. Other crop such as pineapples is manipulated to resist black heart, bananas and papayas for delayed ripening and chili for virus resistance. Malaysia is also developing genetically engineered oil palm with a focus on increasing value-added products from the palms such as high oleate and high stearate oil, nutraceuticals (vitamin A and vitamin E) biodiesel and bioplastics. Genetically modifying technology has been in introduced to assist the development of animal husbandry. Besides that, Malaysia has released 6,000 genetically modified mosquitoes designed to combat dengue fever at an uninhabited site in the central state of Pahang. The biotechnology sector faces a challenging future with increasing global competition. Malaysian government will, under the ninth Malaysia plan, implemented the strategic thrust of the national biotechnology policy, with the active participation of private sector. With the recognition as the worlds halal hub, and given importance attached to the biotechnology industry, Malaysia is poised to introduced biotechnology products with GM label and halal certification. 6. Conclusion In the future, there would be a wide range of crops that are resistant to pest, diseases, and herbicides. The crops would also be high in nutrition value to suit our body system and could be designed to accommodate whatever type of climate changes. The future of GMO is still yet far to go. GMO is a giant leap in the agricultural sector. It is now up to us to decide on how GMO should be used, whether for the good of mankind or the destruction of us all.

Conclusion On Foot Reflexology Health And Social Care Essay

Conclusion On Foot Reflexology Health And Social Care Essay This study was undertaken to determine the effectiveness of foot reflexology in terms of enhancing psychological wellbeing of elderly people in selected old age home at Pondicherry. Ageing is the accumulation of changes in an organism or object over time. Ageing in humans refers to a multidimensional process of physical, psychological, and social change. Health is vital to maintain well-being and quality of life in old age and is essential if older citizen are to continue making active to society. Problems of the ageing are mostly not due to age but largely due to psychosocial environment, diminishing supports and changes in life situations. According to traditional medicine each foot has over 7,000 nerve endings, 26bones, 107 ligaments and 19 muscles. This type of drugless therapy creates a physiological change in the body by naturally improving your Circulation, which reduces our body Tension and enhances relaxation. It aids in the elimination of the body waste and restoring the body functions to better health. The objectives of the study were To assess and compare the pre and post level of psychological wellbeing of experimental group. To assess and compare the pre and post level of psychological wellbeing of control group. To compare the pre test level of psychological well being between experimental group and control group.. To compare the post test level of psychological well being between experimental group and control group. To associate the pre test level of psychological wellbeing among elderly with their selected demographic variables To associate the post test level of psychological wellbeing among elderly with selected demographic variables. The research hypothesis stated were There is a significant difference between the pre test and post test level of psychological well-being among elderly in experimental group at p

The True Gentleman of Great Expectations :: Free Great Expectations Essays

The True Gentleman of Great Expectations To determine if someone is a gentleman, one must look within them and not focus upon their material wealth. In the novel Great Expectations, by Charles Dickens, three characters show qualities of a true gentleman. Pip, Joe, and Provis have true gentlemen-like characteristics, which are shown through the way they live and present themselves. Pip's actions towards others are those of an authentic gentleman. For example, when Provis is very ill and Pip is very kind and says, "I will never stir from your side" (891). This shows that Pip is willing to forget his own comforts and future plans to sit by Provis's side, making Provis's last days on earth comfortable. In addition, Pip saves Miss Havisham when she gets caught on fire: "I had a double-caped coat on...and I got them over her" and "she was insensible and I was afraid to have her moved or even touched" (875). This proves that Pip cares for other people, even if they have treated him poorly. When Pip helps Miss Havisham, it shows his consideration to those in need. Pip relieving Miss Havisham from the fire after she was "coarse and common" towards him, shows Pip has a favorable heart. In conclusion, Pip's behavior towards others is that of a gentleman because Pip treats others with tenderness and affection. Joe's actions are those of a true gentleman. For example, Joe defends Mrs. Joe from Orlick even though he is scared of Orlick himself: "What could the wretched Joe do now...but stand up to his journeyman...so, without so much as pulling off their singed and burnt aprons, they went at one another, like two giants" (773). Joe is intimidated by Orlick and by Joe defending Mrs. Joe from Orlick shows that Joe has courageousness. Joe is a benevolent person by stepping up to Orlick to help Mrs. Joe. In addition, Joe pays off Pip's debts and Pip finds "a receipt for which they had been paid off" (899). Joe paying off Pip's debts shows he is a helpful and caring person. Joe is being considerate by helping Pip become debt-free. It is ironic that Joe helps Pip because Pip hasn't been a considerate person to Joe but he helps Pip regardless.

I have been asked to investigate how the temperature of an experiment E

I have been asked to investigate how the temperature of an experiment affects the rate of reaction. In the experiment I will do it as the temperature of the hydrochloric acid. How Does the Temperature Affect the Rate of Reaction? Introduction I have been asked to investigate how the temperature of an experiment affects the rate of reaction. In the experiment I will do it as the temperature of the hydrochloric acid. Reaction rates can be explained by the Collision Theory. The rate of reaction depends on how often and how hard the reacting particles collide with each other. Basically the particles have to collide in order to react. If the temperature is increased, the particles will have more energy and so will move quicker. If they're moving quicker, they will have more collisions. Planning ======== Variables --------- The variables that may affect my investigation are:  · The temperature  · The size of the pieces of marble chips  · How much hydrochloric acid you use in the flask The variable that I am going to investigate is the temperature. This is because there is more of an advantage due to the fact that there is more of a range of temperature than there is in the size of marble chips you use or the amount of hydrochloric acid you use. Prediction I predict that when I increase the temperature of the experiment, the reaction will take place faster. This is because when the temperature increases, the particles will all mov...

Century In Canada

Nations are born out of conflict, and grow and thrive by learning from their mistakes. The 20th century in Canada was responsible for an abundance of great aspects that now exist in our country. Within that era the rights of women were recognized and altered, resulting in them being considered equals to men. Our army became recognized as an elite fighting force. Japanese Canadian internment camps were put in place as a result of the bombing of Pearl Harbor displayed nothing less then an unjust act.All leading up to the passing of the Canadian Charter Of Rights And Freedoms making certain that inhumane acts that have happened in our past will not happen again. After all, those who do not learn from their mistakes are doomed to repeat it. The early years of the 21st century were important to shaping Canada as a nation. 2 major events occurred during this time that helped to create our identity; the feminist movement began to take hold within and beyond our borders, as well as beginning to be recognized as a world-class military force.Women (prior to the famous five) were tremendously discriminated against and viewed as incapable of doing many acts. Emily Murphy, a self-taught legal expert, who championed in women and children's rights felt strongly in fighting for gender equality. In 1903 she began a campaign focusing on property rights of married women. With her hard work and dedication in 1911 the Dower Act was passed. The act stated that women had the right to one third of their husband's property and allowed for the surviving spouse to become the legal owner of the home.This signified a huge step for women because it proved there rights were beginning to be recognized and there was hope for one day being considered equals to men. Her career continued to progress when she along with other concerned women attended a trial for Edmonton prostitutes on October 17, 1933. The women were ordered to leave the court because the case was not to be viewed by â€Å"mixed company'. Murphy was furious and proposed that if women weren't allowed to view the case there should be a separate court for women, run by women.Emily later went on to become a Judge, Just like the generations of male lawyers/Judges in her family. Emily had to cope with the hurtful remarks from male lawyers questioning how she can be a Judge, and therefore be granted powers o make important/ valuable decisions, if she is not even considered ‘a person'. The law essentially categorized women as ‘crazy, unstable lunatics' and not considered a person. This got her fuming, fighting until there was Justice. Murphy gathered up 4 other women with the same political views as her, and together they made up the famous five.Emily, Henrietta Edwards, Irene Parlay, Louise McKinney and Nellie McClure were all strong willed women coming from well educated backgrounds and were devoted to social change and women suffrage. With the support of the female citizens they produced a petition and brought it to the Supreme Court. After a nail biting 5 weeks of debates the petition was denied. The women however were not discouraged and delivered the petition to Britain Privy Council, the highest role of government in Canada.On October 18, 1929 the Privy Council announces the Persons Case, explaining that women were legally considered persons and therefore could become members of the Senate of Canada. There is no question about it this milestone was the first of many for Canadian women, and because of the efforts of the Famous Five's women would now be considered equals to their male counterparts. The women of today owe a tremendous amount of gratitude for their efforts. World War I lasted from July of 1914 to November of 1918. During this time Canadians began to build an identity for themselves.This is evident during the battle of Vim Ridge. Canadian troops were ordered by Britain to conquer Vim Ridge, a prime piece of land that would be critical to the allies' efforts. Un fortunately the Germans had control over it, but Canadian troops lead by General Bang and General Currie were going to set out to conquer the ridge. Prior to the planned invasion the Canadian troops had to undergo weeks of exhausting practice drills, as it was crucial o stay undetected and surprise the enemy and that everything was executed perfectly, or the whole mission would be Jeopardized.Canadian aircrafts flew overhead the ridge and photographed what the ridge looked like. Returning back to Canadian grounds with information in hand this allowed for Canadian forces to set up an exact replica of what to expect during the attack in terms of characteristics of the ridge, and where the Germans were standing guard. Troops trained for weeks on the recreated Vim Ridge set, until they knew it so well they could perform their duties blindfolded. The Canadian forces had also set in place 2 techniques that would help them take over the ridge after they emerged from the tunnels being built to get as close as they can.They then would execute the creeping barrage and vim glide. The strategy consisted of making a smoke screen in front of them (produced by bombs) and crawling low to the ground, placing them beyond enemy lines. This allowed for the forces, when they were ready to attack, to take the enemy by surprise and hopefully conquer. On April 9, 1917 all 4 divisions of Canada's troops attacked, he plan was executed exactly as planned and the Canadians conquered the ridge. However, this battle was a tragic one as Canada was faced with heavy casualties, resulting in 3600 soldiers killed.The victory for Canada resulted in a nation and its armed forces being recognized for their brave men as well as smart planning and execution. Because of Vim Ridge we began to be a nation worth fearing. After the horror of the First World War and the tremendous achievement for women's rights, Canada was a nation well on it's way to great success. Though the war was devastating, we ulti mately came out of it stronger. Moving into the ass's women roles were continuing to evolve. The flapper girl age was beginning.What brought upon this revolution was the fact that during the war women had to disobey societies views on what a women should and should not do by stepping up and performing the boys jobs while they were off serving in the war. They had to remove their aprons, and leave the stove. This was a time they needed to step up and take over their husband's jobs in order to still provide for their family and be able to put dinner on the table. Once the war had ended women were not going to return back to their old roles. Women didn't want, and didn't feel like, they needed to succumb to society.They were comfortable in their new lives, though it was only intended to be temporary. This new wave of young women wanted to stand out and be different. All of these factors birthed the flapper girl. She appeared as a boy, dressed with short hair, higher skirts, and flatten ed chests. They had a strong appearance and attitude about them they felt liberated. The younger generation saw the time frame as a perfect opportunity to introduce this new style, given that women's rights were evolving, this would bring more attention onto them. It was overall a rebellious movement of expectations of women. (http://history sass. About. Mom/odd/sass/a/flappers. HTML) After the Japanese attacked Pearl Harbor, Hawaii on December 7, 1941 Canada took a step backwards on human rights and discrimination against the Japanese. At the time there were 22,000 Japanese Canadians living in British Columbia, some of wham's ancestors were the first immigrants coming for work to Canada in the sass. Though they had always been discriminated against by the largely white Canadian society, it was nothing compared to what was about to come. Days after the Pearl Harbor attack, Canadian companies began to fire all Japanese workers beginning with the Canadian Pacific Railways.Matters got worse when Japanese forces attacked Hong Kong and killed over 2000 Canadian soldiers stationed there for training. The Japanese began to be referred to as SAPS, and signs were being posted around the province harshly stating, â€Å"Keep out†. It was then the Federal Government designated a 100-mile wide strip, as a protected area to keep all Japanese until they would be further placed inland. They were finally ordered to pack a small suitcase and live in inverted over animal stalls awaiting their train to arrive. (http://www. CB. Ca/history/ OPPOSITENESS EPOCH APPEAL. HTML). Husbands, wives and children were all separated. The men were sent to work on road gangs, whereas the women and children were sent to shantytowns in the B. C wilderness. In January of 1943 the government forced the sale of all property/ belonging to the Japanese Canadians that includes their homes, cars and other valuables. The reasoning behind this was to erase any memories the Japanese built in Canada a nd to convince them not to assume living here when the war over. The writing was essentially on the walls, the Japanese were no longer welcome.Once the war ended the B. C federal government decided to release all Japanese from the camps. The Japanese were then faced with choosing between deportations back to Japan, specifically parts that were destroyed during the war, or moving east into the Rocky Mountains. The majority of them chose to move to Ontario, Quebec and the Prairies. Many families did move back to Japan as well. It was a long time coming, but finally on April 1st, 1949 after much protest, Japanese Canadians were finally allowed the freedom to live anywhere in Canada.

Game Theory and Life Insurance

Astln Bulletin 11 (198o) 1-16 A GAME T H E O R E T I C LOOK AT L I F E I N S U R A N C E UNDERWRITING* JEAN LEMAIRE Universit6 Libre de Bruxelles Tim decision problem o[ acceptance or rejection of life insurance proposals is formulated as a ~vo-person non cooperattve game between the insurer and the set of the proposers Using the mmtmax criterion or the Bayes criterion, ~t ~s shown how the value and the optunal stxateg~es can be computed, and how an optimal s e t of medina! , mformatmns can be selected and utlhzed 1. FORMULATIONOF THE GAME The purpose of this paper, whose m a t h e m a t i c a l level is elementary, is to d e m o n s t r a t e how g a m e t h e o r y can help the insurers to formulate a n d solve some of their underwriting problems. The f r a m e w o r k a d o p t e d here is life insurance acceptance, but the concepts developed could be a p p h e d to a n y other branch. The decision problem of acceptance or rejection of life insurance proposals can be f o r m u l a t e d as a two-person non cooperative g a m e the following w a y : player 1, P~, is the insurer, while player 2, P2, is the set of all the potential pohcy-hotders. The g a m e is p l a y e d m a n y times, m fact each time a m e m b e r of P. – fills m a proposal. Ve suppose t h a t tlfis person is either perfectly h e a l t h y (and should be accepted) or affected b y a disease which should be detected and cause rejection. We shall assume for the m o m e n t t h a t the players possess only two strategies each. acceptance a n d rejection for P~, health or disease for P2. To be more realistic we should introduce a third pure s t r a t e g y for P~: a c c e p t a n c e of the proposer with a surcharge. To keep the analysis as simple as possible we shall delay the introduction of surcharges until sectmn 4. Consequently we can define a 2 x 2 p a y o f f m a t r i x for the insurer. .P~ †¢ P2 healthy proposer A B ill proposer C D acceptance rejection I t iS evident t h a t the worst o u t c o m e for the insurer is to accept a b a d risk. I n t e r p r e t i n g the payoffs as utilities for P1, C should be the lowest figure. Clearly D > B : it is better for the insurer to reject a b a d risk than a good risk. Also A must be greater t h a n B. One anight argue a b o u t the relative * Presented at the 14th ASTIN Colloqumm, Taornuna, October x978. 2 JEAN LEMAIRE values, A and D, of the good outcomes. We shall suppose in the examples and the figures that D > A, but the analysis does not rely on this assumptmn. In order to find the value of the game and the optimal strategy for P~, we can apply – – the minimax criterion, or – – the Bayes criterion. 2. THE MINIMAX CRITERION To apply the minimax criterion assimilates P2 to a malevolent opponent whose unique goal is to deceive the insurer and to reduce his payoff. This is of course an extremely conservative approach, to be used by a pessimistic insurer, concerned only by its security level. 2. 1. Value and Optimal Strategies without information Since P2's objective is to harm P~, the game becomes a 2 x 2 zero-sum twoperson game, which can be represented graphicaUy. The vertical axis of fig. 1 is the payoff to P1. His possible choices are represented by the two straight lines. The horizontal axis is P2's choice: he can always present an healthy proposer, or a non healthy, or pick any probability mix in between. The use of mixed strategies is fully justified here since the game is to be played m any times. Since P2's payoff is the negative of Pl's', his objective is to minimize the insurer's maximum gain, the heavy broken line. The ordinate of point M Payoff Io p~ D A B healthy i'x~n hi'Klllh Fig. i LIFE INSURANCE UNDERWRITING 3 is then the value of the game. The abscissa of M provides the optimal mixed strategy of P2 P~'s optimal strategy can be obtained similarly (for more details see for instance OWLN (1968, p. 29) ) Thus, by adopting a mixed strategy (to accept any risk with a probability D-B PA = A + D – B – c ‘ and t  ° reject w i t h a p r o b a b i l i t y p n = I AD-BC ? ‘A),. P~ can guarantee himself a payoff of v~ = A + D – B – C ‘ D-C PH = A + D – B – C whatever the strategy adopted by his opponent. P2's optmml strategy is to present a proportion of good risks. 2. 2. Introduction of Medical Information The preceding model is extremely naive (and vv1Lt only be used as reference for comparisons) since it does not take into account P,'s possibility to gather some information about the proposer's health, by asking him to fill in an health questmnnaire, or by requiring him to undertake a medical examination. This information is of course only partially reliable. But, however imperfect, it can be used to improve P~'s guaranteed payoff. How can the insurer make optimal use of the information lie does have ? It is sufficient for our purposes to characterize tile medical information by two parameters : Ps, tile probability of successfully noticing a bad risk, and PF, tile false alarm probability of detecting a non-existant illness. Let us introduce a third pure strategy for P , : to follow the indications of tile medical information. If tile proposer is not healthy, his illness is detected with a probabihty Ps, and remains undetected with a probability 1 – – P S . . P i ‘ S expected payoff thus equals E = Dps + C(1-ps). Smailarly, his payoff m case the proposer is healthy is F = (1–pF)A + t~FB. Fig. 2 represents a â€Å"detector† with a . 7 success probability and a . 4 false alarm probability. We notice that, m this case, P1 can guarantee himself a payoff v2 > vl by mixing the strategies â€Å"to accept† and â€Å"to follow the detector's indication†. Of course, for other values of Ps and PF, tile optimal mixed strategy varies and can mix a different set of pnre strategies. The detector can even be so imperfect that the line . FE passes below the intersection of B D and AC; then the medical information is so weak that it is useless. 4 Payoff to Pl JEAN LEMAIRE JD1 J E~ ao % 7o % 4o % 6o % I A. healthy f~n heall hy Fig. 2 2. 3. Optimal Deteclwn System A detector is characterized by a pair (Ps, PFF) of probabilities. The underwriters can decide to render the standards of acceptation more severe, by rejecting more people, thereby incrcasing the success probabihty Ps. Unfortunately, the false alarm probability PF will then increase too. Can gaine theory help us to select an optimal detection system ? Must the company choose a â€Å"nervous† detector, with a high success probability, but also a high false alarm rate, or a â€Å"pldegmatic† or â€Å"slow† system with low probabilities Ps and PF ? Let us assume for sunplicity that all the medical information has been aggregated mto a single discriminating variable (for instance by using discrlminant- or regression analysis). The distribution of the discriminatmg variable for the healthy population will usually overlap the dastribution for the non healthy group. The choice of a particular detector can consist of selecting a critical value, any higher observed value leading to rejection, any lower value to acceptance (this procedure is optimal if the distributions are normal with equal variances Otherwise, tile decision rule can be obtained by a hkelilaood ratio method (see appendix or LEE (1971, pp. 2oi-2o3)). The shaded zone represents the false alarm probability, the dotted region the success probability. Each critical value determines those two probabilities. If the critical value is moved to the right, the detector becomes slower. If it is moved to the left, it become~ more nervous. The set of all the critical values LIFE INSURANCE UNDERWRITING healthy [ non healthy value acceptance t | of the t n g variable dlSCrlmlnat relectlon Fig. 3 Y Ps Fig 4 defines the efficiency curve of the d i s c n m i n a n t variable. The weaker the dlscriminant power of this variable, the nearest to the bissectmg line its efficiency line. A perfect discrimmant variable has a triangular efhciency x y z . The set of all the detectors determines a set of values for the game. The highest value v* for the insurer is reached when the p a y o f f line is horizontal. This can be roughly seen as follows (for a more rigorous proof see LUCE and RAIFFA (1957, pp. 394-396)): the critical value, m o v i n g from left to right, generates a family of hnes with decreasing slope. If . Pat chooses a d e t e c t o r with 6 JEAN LEMAIRE a pos~ttve slope, P= can reduce his payoff below v* b y always presenting h e a l t h y proposers. Similarly, ~f the slope is negative, a continuous flow of non h e a l t h y proposers will keep P~'s payoff below v*. yotl to Pt I D A C h , a i r h~ rmn heulth, Fig 5 The optimal detector can be easdy obtained b y equating the payoffs E and F : Dps + C ( 1 – p s ) = A ( l – p y ) Then (1) + BpF. D-C C-A PF – B – A PS + B – A defines a straight line in fig. 4, whose intersection with the efficiency line determines the o p t i m u m . N o t e t h a t the optimal s t r a t e g y of P~ is a pure s t r a t e g y : to follow the advace of the d e t e c t o r , the insurer does not have to t h r o w a coin after the mecidal examination m order to decide if tile proposer is accepted. W h a t happens is t h a t the â€Å"noise† in the observation system, however small, provides the necessary r a n d o m i z a t i o n in order to p r e v e n t P2 from outguessing the insurer. 2. 4. The Value of Improving the Detectton System A medmal e x a m i n a t i o n can always be improved† one can introduce an electrocardmgram, a blood test . . . . for each proposer. B u t ~s it w o r t h the cost ~ An i m p r o v e d discrimination ability means t h a t tile distributions of fig. 3 are more LIFE INSURANCE UNDERWRITING 7 Fig. 6 Payoff to p, D A im rn i ir~f r m i n B C healthy on hl, olt h Fig. 7 separated and present less overlap. The characterizing probabilities ibs and PF are maproved, and the efficiency line moves away from the bisecting line. The intersection of the improved efficiency line with (1) (which is determined only by the payoffs and therefore does not change with increased discrimina- 8 JEAN LEMAIRE tion) provides the new optimal detector; the ass ociated value is higher for the insurer. If the cost of implementing the new system is less (in utilities) than the difference between the two values, it is worthwhile to introduce it. The insurer should be willing to pay any amount inferior to the difference of the values for the increase in lus discrimination ability. 2. 5. A n Example 1 All the proposers above 55 years of age willing to sign a contract of over 3 million Belgian Francs in a given company have to pass a complete medical examination with electrocardiogram. We have selected 200 male proposers, loo rejected because of the electrocardiogram, and loo accepted. This focuses the attention on one category of rejection causes: the heart diseases, and implicitly supposes that the electrocardiogram is a perfect discriminator. This (not unrealistic) hypothesis being made, we can consider the rejected persons to be non healthy. Correspondingly the accepted proposers will form the healthy group. We have then noted the following characteristics of each proposer: x~: overweight or underweight (number of kilograms minus number of centimeters minus loo) ; x2: number of cigarettes (average daily number); m: the presence of sugar x4: or albumine in the urine; x s : the familial antecedents, for the mother, xs† and the father of the proposer. We then define a variable x0 = l o if the proposer is healthy 1 otherwise nd apply a standard selection technique of discriminant analysis in order to sort out the variables that slgnihcantly affect Xo The procedure only retains three variables xj, x2 and m, and combines them hnearly into a discriminating variable. The value of this variable ~s computed for all the observatmns, and tile observed distributions are presented in fig. 8. As was expected, the discrimination i s quite poor, the distributions strongly overlap. The multiple correlation between Xo and the set of the explaining variables equals . 26. The group centroids are respectively . 4657 and . 343We then estmaate for each possible crltmal value Ps and PF and plot them on fig. lo. t This e x a m p l e p r e s e n t s v e r y w e a k d e t e c t o r s a n d is o n l y i n t r o d u c e d m o r d e r to illus t r a t e t h e p r e c e d m g theory. LIFE INSURANCE UNDERWRITING 9 Fig 8 S Fig 9 We must now assign uNhtlcs to the various outcomes. We shall select A = 8, B = 4, C = o and D = lo. Then the value of the g a m e w i t h o u t medical information is 5. 714, P2 presenting 2/7 of bad usks and P i accepting 3/7 of the proposals. Let us now introduce the medmal reformation nd for instance evaluate the s t r a t e g y t h a t corresponds to a . 5 critical value. On fig. lO, we can read ~s = . 51 a n d PF = 33. Then E = . 5] ? ]o + . 4 9 x o = 5-], a n d F = 3 3 x 4 + . 67 x 8 = 6. 68. The value of this game is 6 121, P2 presenting more bad risks (34. 1%), P I mixing the strategies † r e j e c t † and â€Å"follow d e t e c t o r † with respect- 10 JEAN LE/vIAIRE F i g . 1o Fig. 11 LIFE INSURANCE UNDERWRITING 11 lye probabilities . 208 and . 792 Fig. 11 shows t h a t this s t r a t e g y is too â€Å"slow†, t h a t too m a n y risks are accepted. On the other hand, a detector w~th a . 4 critical value is too nervous: too m a n y risks are rejected T h e value is 5. 975, P2's optimal s t r a t e g y is to present 74. 7% of good risks, while Pa should accept 29. 7% of the tmle and trust the d e t e c t o r otherwise. To find the o p t i m u m , we read the intersection of the efficiency line with equation (1), in this case 5 ~F = 2 – 2 Ps We find PF = . 425 Ps = . 63 with a critical value of . 475. T h e n E = lOX. 63 + ox. 37 = . 425Ãâ€"4 + – 5 7 5 x 8 = 6. 3. f the insurer adopts the ptu'e s t r a t e g y of always accepting the a d w c e of the medical information, he can g u a r a n t e e himself a value of 6. 3 irrespective of his o p p o n e n t ‘ s strategy. L e t us now a t t e m p t to improve the me examination b y a d & n g a new variable xT, the blood pressure of the proposer Because of the high positive correlation between xt and xv, the selection procedure only retains as significant the varia bles x. % xe and x7 Fig. 9 shows t h a t the distributions are more separated. In fact, the group centroids are now . 4172 and . 828 and the multiple correlation between xo and the selected variables rises to . 407. T h e efficiency hne (fig IO) is uniformly to the right of the f o r m e r one. The intersection with (1) is PF = 37 P,s = . 652 with a critical value of approxunatxvely . 45. The value of the game rises to 6. 52, an i m p r o v e m e n t of 22 for the insurer at the cost of controlling the blood pressure of each proposer (see fig. 1~). 3' THE BAYES CRITERION I n s t e a d of playing as if the proposer's sole objective were to o u t s m a r t him, the insurer can a p p l y the B a r e s crlter~on, i. . assume t h a t P2 has a d o p t e d a fixed a priori s t r a t e g y H e can suppose (from past experience o1†³ from the results of a sample s u r v e y p e r f o r m e d with a m a x n n a i me&cal examination) t h a t a p r o p o r t i o n Pn of the proposers is hea lthy. The analysis is easier m this 12 JEAN LEMAIRE case, since P2's m i x e d strategy is now assumed to be known P t only faces a one-dimensional p r o b l e m ‘ he must maximize his utility on the d o t t e d vertical line of fig. 12. Pc/Of f p~ to JD A t B, N C ol eall hy 1 – PH PH non heoll hy Fig 12 One notices from fig. 12 t h a t a medical examination is sometimes useless, especially if PH is near 1. In this case, P t ‘ s optimal s t r a t e g y is to accept all the proposers. In the general case, P t should m a x m n z e the linear function of PF a n d PH [~5FB + (1 – – pF)A]~SH + [paD + (I – ps)c] (1 – PH), under the condition t h a t PF and Ps are linked b y the efficiency curve of fig. 4. As far as the example is concerned, this economic function (represented in fig lo) becomes 1. Ps – 3 4PF if one supposes that p2's mixed s t r a t e g y is to present 15% of bad risks. 6. 8 + F o r the first set of medical informatio n (xl, x2, x6), tile m a x i m u m is reached at the point Ps = . 28, PF = . 09. Since PH is r a t h e r tngh, this is a v e r y slow detector, yielding a fmal u t d l t y of 6. 914. Comparing to the optimal n n x e d strategy, this represents an increase in utility of . 614, due to tlie exploitation of . P2's poor play. Of course, tliis d e t e c t o r is only good as long as P2 sticks to LIFE INSURANCE UNDERWRITING 3 his mixed strategy. It is uneffective against a change in the proposers' behaviour: if for instance PH suddenly drops below . 725, P~'s utlhty decreases under 6. 3, the guaranteed payoff with the mlmmax strategy In this aspect, the Bayes criterion implies a more optimistic attitute of P1. For the second set of medical information (x2, m, xT), the opblnal detector (Ps = . 45, ~bF = o9) grants a utility of 7. t69 if PH = . 85, an improvement of . 649 colnparing to the ininimax strategy (see fig. 11). 4. T O W A R D S MORE R E A L I S M 4. 1. Surcharges Conceptually, the introduction of the possibility of accepting a proposer with a surcharge presents little difficulty: it amounts to introduce one more pure strategy for the insurer. Payoll to ID A G B heollhy non heoil hy F , g . 13 A detector could then be defined by two critical values C1 and C2 enveloping an m c e m t u d e or surcharge zone. The two critical limits would detelmme 4 probabihtles fl~ f12 p8 p4 = = = = probability probabihty probability probability of of of of accepting a bad risk surcharging a bad risk rejecting a good risk surcharging a good risk 14 JEAN LEMAIRE ealthy non healthy V Surchar~le I C1 C2 Fig. 14 and two efficiency curves. A necessary condition for a detector to be optimal is that the corresponding payoff hne is horizontal, i. e. that (2) (1–[email  protected] + 7b,G + p3B = ( 1 – p ~ – p 2 ) D + P2H + P~C. The two efficiency curves and (2) determine 3 relations between the probabilities. One more degree of freedom is thus avai lable to maximize the payoff. 4. 2. Increaszng the Number of Strategies of P2 In order to practically implement the preceding theory one should subdivide P2's strategy â€Å"present a non healthy proposer† according to the arious classes of diseases. P1 should then have as pure strategaes: reject, accept, a set of surcharges, and follow detector's advice, and P2 as m a n y pure strategms as the number of health classes. The graphical interpretation of the game is lost, but linear programming fan be used in order to determine its value and optimal strategies. Appendix: The Likehhood Ratio Method Let — x be the value of tlle discriminant variable, healthy, – – p(H) and p(NH) the a priori probabihties of being healthy or non – – f(x I H) and f(x ] NH) the conditional distributions of x. We can then compute the a posterior1 probability of being non healthy, given the value of the discriminant variable (1) p = p ( N g ix) = f(x l g H ) p ( N H ) f(x l N H ) p ( g g ) + f ( x l H)p(H)† LIFE INSURANCE UNDERWRITING 15 Similarly p ( H I x) = l – p. T h e e x p e c t e d payoffs for the two decisions are EPA = ( 1 – p ) A EPR = (1-p)B Define D* to be D* = EPA — + pC + po. EPn = [(A-B)+(D-C)]p – (A-B). Consequently, D* is a linear function of p, with a positive slope. There exists a critical ~b, ~b,, for which D* = o' (A – B ) Pc = ( A – B ) + ( D – C ) nd the optimal decision rule is to reject if p > Pc ( t h e n D * > o ) a n d t o – – accept if p < Pc (then D * < o ) . — If f ( x [ H) and f(x I N H ) are normal densities with equal variances, there is a one-to-one m o n o t o n i c relationship between p and x, and thus the crttmal p r o b a b l h t y Pc induces a critical value xe. In general, h owever, the cutoff point is not unique. T h e r e m a y be two or more critical values. In t h a t case, we define the likelihood ratio of x for hypothesis N H over hypothesis H as f(x [ N H ) L(x) Of f(x I H) c o u r s e o _-< L(x) =< oo. S u b s t i t u t i n g L(x) in (1) gives 1 P = or 1 L(x) p ( N H ) + p(H) p 1 (2) L(x) – p ( N H ) l – p † F o r constant a priori probabilities, there is a m o n o t o n e relationship between p and L(x); L(x) goes from o to oo as p goes from o to 1. Therefore, a unique critical likelihood ratio Lc(x) exists and can be obtained b y replacing Pc for p in (2) (3) p(H) A – B Lc(x) – p ( N H ) D – C† ] 6 JEAN LEMAIRE p 1. 0 ~-Pc = 0 5 0. 5 I I I NH H I_-~ X? I J_ X? 2 H — Fig. 15 The optimal decision rule reads if L(x) > L c ( x ) , reject; if L ( x ) < L c ( x ) , accept. Notice that, i f A – B = D – C , pc = 1/2 The decision rule is equivalent to maximizing the e x p e c t e d n u m b e r of correct classifications. F r o m (3) p(H) L e(x) #(NH)† If, furthermore, the prior probabii]ties are equal, Lc(x) = 1. REFERENCES AXELROD, 1~ (1978) Copzng wzth deception, International conference on applied game theory, Vmnna LEE, V,r. (1971) Dec~szon theory and human behaviour, J. Wiley, New York LuCE, R and H ]{AIFFA (1957). Games and deczszons, J Wiley, New York. OWEN, G. (1968) Game theory, ~V. Saunders, Philadelphia.