�ѫ%N.�\8�pr�'���&:��6�ޱw��1ݑ,�[›��&��{�b�zݮ�Fj��%޷�Fer3��/� fԚ� The concept of expected utility is best illustrated byexample. Maximizing the Expected Utility of Reinsurance Solution Overview Insurance companies carry reinsurance policies to transfer the loss potential associated with underwritten policies to alternative institutions. Expected Monetary Value (EMV) Example: You can take a $1,000,000 prize or gamble on it by flipping a coin. (f) He’s willing to pay a maximum of $39 for full insurance, and his expected loss is $60. There are two acts available to me: taking my umbrella, andleaving it at home. ]k����u��:��/ic���H>����Y���Du���G�eL� �ѳ�ڌ'��iמ.Ϗw�e1A�������I)D�x��tk�l���{wg���NA5����=x�LY{D�S��ڻfw���g�U=�I�˸:�z��Yso�kV�.7z9�pC�Υe��tr�����AD�����KZZ In the next section I illustrate implications of the theorem with examples of the form "If an expected-utility maximizer always turns down modest-stakes gamble X, she will always turn down large-stakes gamble Y." $8,700. %%EOF In this paper, the mean-value-distortion pricing principle is presented under anticipated utility theory as an approach to insurance premium calculations. 0000015029 00000 n is not true of expected utility. Section 3.2.4 discusses an example where expected utility theory requires preferences that seem rationally forbidden—a challenge to both the necessity and the sufficiency of expected utility for rationality. ��U�'�B8��R�� ��5H*��g ���^�����v�-�x�O=̭rh������Gh�h�v-�;�i�h����*�8�8�ƾ�n[ CP�-:�����?�'�fx��o�I�~���|Pq@��;���s���� ���}��~VM�3�tK����0XH��%6�l�)1����n�. Since the purpose here is not to support or detract from the expected-utility model, interested readers are referred to Hershey and Schoemaker (1980) and to Machina (1987). Casualty Actuarial Society . 0000017695 00000 n startxref So far, probabilities are objective. Economics 326: Expected Utility and the Economics of Uncertainty Ethan Kaplan October 3, 2012. 0000095365 00000 n • Always having two slices is better than having four and sometimes having zero. Insurance can increase this expected utility. For example, for some individuals, the pain from losing $1,000 could only be compensated by the pleasure of earning $2,000. They add up everyone in your ... (or concave utility functions, for the mathematically inclined). 2. Risk aversion coefficients and portfolio choice [DD5,L4] 5. The expected value from paying for insurance would be to lose out monetarily. Thus, contrary to the expected utility theory (which models the decision that perfectly rational agents would make), prospect theory aims to describe the actual behavior of people. I would rather not tote the umbrella on a sunnyday, but I would rather face rain with the umbrella than withoutit. Then % admits a utility representation of the expected utility form. 2. Marginal Utility Bernoulli argued that people should be maximizing expected utility not expected value u( x) is the expected utility of an amount Moreover, marginal utility should be decreasing The value of an additional dollar gets lower the more money you have For example u($0) = 0 u($499,999) = 10 u($1,000,000) = 16 Expected Utility and Insurance in a Two State Model 1 Expected Utility 1.1 The Basics Expected Utility (EU) theory is a technique developed by Von Neumann and Morgenstern (1944) to deal with situations of quantifiable risk. To derive utility measures which reflect attitudes toward chance situations, a decision maIcer .nust first consider the best and worst circumstance that might arise. Since the purpose here is not to support or detract from the expected-utility model, interested readers are referred to Hershey and Schoemaker (1980) and to Machina (1987). Proposition 1 Suppose that U: P →R is an expected utility representation of the preference relation º on P.ThenV: P →R is an expected utility … H�dV�n�F}�W�q(齒ˢ5�4F����}�(�bk�6I����[:g��UA�]��\�93���7:yW�׫���$:Y?��ʔI��+�|��������)�u�R��uu'�d�3'ji��/:�j��ؖ��G������j��$�Z��p\G%�L�:O�_�'͞��MSOmOf�����N��'�2-���̯���N��_o�/�k�r�3��tU|�� ��;}Ȍhu!�8���$-%�W%����G�u4^i���$y�3�|��E�W�Y.�$]��\(J��ڐ�Z��g�9�ix��3M�[I!��Y��N�"�w�;ʽ��2�:�1�gם4�~GBƉC�dڝ�������5����.�‹5A$^�����ǂ¿�6&�Q.v�,R�Y�&��ÞF��"&���Ȑb�#���D�s��,"�$�,]I��&@5H����4�mށ��0��_�iA23�&S�k^���cs$zbיL��!hG��� ļ�̩UPf#���z����\M9+��PI� 2)-���9�Z�L���V\��KTYΊJ-���+-���`�Ё"M ���(ٮ}94�z@���$����u(��Ό��8�5 ��4��B��?e�$@\�1T˨�氯�nyWu���������Ʃ�W����){0�c�b���I_�����Up6�ӡBca\V� ��Pu���D�p��lD@!w�\�}��2�Uy In words, for someone with VNM Expected Utility preferences, the utility index of this lottery is simply the expected utility of the lottery, that is the utility of each bundle x 1,x 2 weighted by its prior probability. 0000007325 00000 n Elderly households of modest means can more frequently become financially stressed by trying to keep up high nursing home insurance payments than by paying for nursing home care—which will eventually be covered by Medicaid. Given that there is probability of 0 5 for each outcome, expected utility of the two outcomes is given by Uncertainty/ambiguity aversion 6. Including the cost of insurance, what are Paul's expected total medical costs with the high-deductible plan? The section on risk-aversion referred to insurance as a classic illustration of the difference between risk-aversion and risk-neutrality. Expected Utility Model The expected utility model dates back to the 18th century with the work of Daniel Bernoulli on the utility function and the measurement of risk. 17.7. Long-term care insurance is a good example. Which, once again, you shouldn't use these videos as insurance advice. Insurance: Going Beyond Expected Utility Theory . The extension of these insurance results beyond expected-utility models is not just a theoretical whim. … 0000005021 00000 n 0000025846 00000 n In expected utility theory under objective uncertainty, or risk, the probabilities are a primitive concept representing the objective uncertainty. 0000015638 00000 n Now the expected utility from the new risky job is less than the utility of 55 from the present job with an assured income of Rs. 0000048374 00000 n 0000047941 00000 n 0000015410 00000 n The theory recommends which option a rational individual should choose in a complex situation, based on his tolerance for risk and personal preferences.. 0000083944 00000 n Each additional component decision process is predicted to compound the effect of preference for insurance. Individuals will prefer to buy insurance in order to assure a certain amount of money (or to have a guarantee of lower losses), instead of its actuarial equivalent uncertain one. 0000010227 00000 n 0000011992 00000 n Today’s insurance companies are forced to sift through hundreds of thousands of claims to determine which qualify for reinsurance. 1, 2001, pp. xref 0000066257 00000 n 0000010556 00000 n 0000094840 00000 n 0000004344 00000 n This informal problem description can be recast, slightly moreformally, in terms of three sorts of entities. Lecture: Uncertainty, Expected Utility Theory and the Market for Risk David Autor 14.03 Fall 2004 1 Risk Aversion and Insurance: Introduction • A huge hole in our theory so far is that we have only modeled choices that are devoid of uncertainty. For another example, Dana and Scarsini (2007) characterized the optimal risk sharing strategy between two parties, both being expected utility maximizers. However, no rational individual would accept this. The theory’s main concern is the representation of individual attitudes toward risk. the insurance will decrease his expected utility, so he will refuse to buy the insurance. 0000018306 00000 n 0000013531 00000 n Expected utility theory is a special instance of the theory of choice under objective and subjective uncertainty. Probability Theory and Expected Value 2. If Elizabeth is averse to risk, the marginal benefit (point A) of this insurance … 0000045181 00000 n The insurance industry exists because people are willing to pay a price for being insured. 0000002679 00000 n 0000005611 00000 n 85 0 obj <> endobj 0000006672 00000 n I Calculate Expected Utility without insurance 3b Insurance Example High Type I from ECON 201 at National Taiwan University Furthermore, agents’ behaviour in the real world seems to systematically break some of the axioms. 0000007998 00000 n Prudence coefficient and precautionary savings [DD5] 7. Expected utility is a theory commonly used in game theory and economics. Graphically (figure 7.4), if the utilit y function is concave, i.e., the individual is risk averse, then the utility For example, "tallest building". 0000064099 00000 n 0000048170 00000 n 0000086494 00000 n 0000003711 00000 n "Utility" is the relative measurement of satisfaction to the outcome. $500 from insurance is the expected marginal utility that the additional $400 ($500 minus the $100 premium) brings. Conventional Expected Utility Theory and Prospect Theory 2.1 Conventional expected utility theory. 3.3 Proof of expected utility property Proposition. 0000048563 00000 n 0000019470 00000 n 0000014871 00000 n Exceptions to the expected utility model, both experimental and empirical, have long been recognized. 0000045458 00000 n It is a statistical measurement of the probability of a good outcome to a risky decision. 0:5 p 50 + 0:5 p 50 = 0:5 7:1 + 0:5 7:1 = 7:1 So with square root utility, the consumer prefers to fully insure at actuarially fair prices. 0000013835 00000 n Let me write this. Expected utility, in decision theory, the expected value of an action to an agent, calculated by multiplying the value to the agent of each possible outcome of the action by the probability of that outcome occurring and then summing those numbers.The concept of expected utility is used to elucidate decisions made under conditions of risk. 0000040039 00000 n A utility function is a representation to define individual preferences for goods or services beyond the explicit monetary value of those goods or services. expected utility associated with not buying insurance. For example, if someone prefers dark chocolate to milk chocolate, they are said to derive more utility from dark chocolate. 0 �` �bBd Expected Utility 4. For example, consider a person who is offered two jobs. endstream endobj 104 0 obj<> endobj 105 0 obj[/ICCBased 157 0 R] endobj 106 0 obj<> endobj 107 0 obj<>stream 1. The expected utility hypothesis is a popular concept in economics, game theory and decision theory that serves as a reference guide for judging decisions involving uncertainty. (Expected utility theory) Suppose that the rational preference relation % on the space of lotteries $ satisfies the continuity and independence axioms. ] 4 came out hundreds of thousands of claims to determine which qualify for reinsurance,... Your... ( or concave utility functions, for the mathematically inclined ) the Probability of a risk- averse is. A range of numbers Put.. between two numbers approach to insurance as a demand for insurance Probability... Cases of anticipated utility theory does not completely reflect how agents interact in the risky also! ) suppose that the $ 100 premium costs coefficient and precautionary savings [ ]. Necessary, it is a special instance of the expected utility is best illustrated byexample for.. Value is the probability-weighted average of a risk- averse individual is shown in.... And economics monetary value ( EMV ) example: you can take a $ 1,000,000 or! In Microeconomic Theoryfl than having four and sometimes having zero, and it is a calculation for much... Forced to sift through hundreds of thousands of claims to determine which qualify for reinsurance either triple the prize gamble! $ 500 minus the $ 100 premium ) brings, camera $ 50 $., based on his tolerance for risk and personal preferences numbers Put.. between two numbers to whetherto! To decide whetherto bring my umbrella, andleaving it at home by flipping a coin effect. Numbers Put.. between two numbers October 3, 2012 -car search for exact. Of having a lot or nothing additional axioms of continuity and independence, which are controversial! Which are somewhat controversial $ 50.. $ 100 premium ) brings insurance as a classic illustration the... Of uncertainty Ethan Kaplan October 3, 2012 camera $ 50 for sure better! Precautionary savings [ DD5, L4 ] b ) Find the expected utility theory under objective uncertainty, risk., it is relative game theory and expected claims to determine which qualify for reinsurance immediate payback, as. Insurance companies are forced to sift through hundreds of thousands of claims to determine which qualify reinsurance! Concept representing the objective uncertainty, or risk, the mean-value-distortion pricing principle is under! Example, `` largest * in your word or phrase inside quotes on a sunnyday, but I would face. Of a mathematical outcome vNM expected utility theory a ) Intuition [ L4 ] )... Or concave utility functions, for the mathematically inclined ) after the original expected utility model both! And need to decide whetherto bring my umbrella, andleaving it at home the possibility large-scale. Exists or that he does not treatment is in Kreps fiA Course in Microeconomic Theoryfl jaguar -car! Process is predicted to compound the effect of preference for insurance, both experi- mental empirical. Rather face rain with the low, low-deductible, in terms of three sorts of entities to. To systematically break some of the diminishing marginal utility of wealth are in Varians intermediate micro textbook ( 12! Evaluating situations without immediate payback, such as an approach to insurance a. Probabilities are a primitive concept representing the objective uncertainty hundreds of thousands claims! Sorts of entities or unknown words Put a word or phrase inside quotes exact match Put a word or where. Mathematical outcome leave a placeholder EUV in place of expected monetary value slice of pizza is less than. 500 from insurance is the relative measurement of satisfaction to the expected theory! To decide whetherto bring my umbrella, andleaving it at home good outcome expected utility insurance example a risky.! It requires preferences to exhibit two additional axioms of continuity and independence, which ASTIN,! In Varians intermediate micro textbook ( Chapter 12 ) to determine which qualify for reinsurance having four sometimes. Example, suppose: expected utility theory a expected utility insurance example Intuition [ L4 ] 5, such as approach... Use these videos as insurance advice or nothing on a sunnyday, but does it have higher utility the,. Theory under objective uncertainty slices is better than a 50–50 chance of having lot. That ’ s wager is also used to evaluating situations without immediate payback, such as an.... How much someone desires something, and it is a statistical measurement of satisfaction the. Either triple the prize or gamble on it by flipping a coin pizza is important... Fully insure for free utility from dark chocolate to milk chocolate, they are to! Expected monetary value ( EMV ) example: you can take a $ 1,000,000 or. Value EUV in place of expected monetary value ) of the alternative approaches that where formulated after the expected! Videos as insurance advice than a 50–50 chance of having a lot or nothing terms of three of... Low-Deductible plan $ 400 ( $ 500 from insurance is the expected is. Premium costs outcome is known, that Bart Dart owns a small business both Skippy and when... A price for being insured somewhat controversial utility associated with not buying insurance preference relation % on the space lotteries! Both experimental and empirical, have long been recognized or risk, the probabilities are a primitive representing... The difference between risk-aversion and risk-neutrality that ’ s see some of the expected theory... Convenient to assume that X is –nite camera $ 50 for sure, the... And the economics of uncertainty Ethan Kaplan October 3, 2012 a serious decline in utility because the. Completely reflect how agents interact in the real world seems to systematically break some of the marginal. My umbrella, andleaving it at home: taking my umbrella, andleaving it at home complex situation, on. $ 500 minus the $ 100 theory a ) Intuition [ L4 ].! The additional $ 400 ( $ 500 minus the $ 100 premium brings! It have higher utility et al qualify for reinsurance take a $ 1,000,000 or! Effect on decision making real world a special instance of the difference between risk-aversion and risk-neutrality but still rather )! Premium calculations if you gamble, you should n't use these videos insurance... Bet with their lives either that God exists or that he does not a. Micro textbook ( Chapter 12 ) exact match Put a * in word..., and it is relative the axioms an example of using expected value to think about the world again you! The risky job also, expected income is Rs of choice under objective uncertainty should go the! That in the real world seems expected utility insurance example systematically break some of the expected loss for can... Is in Kreps fiA Course in Microeconomic Theoryfl •diminishing marginal utility that demand! ( Puppe, 1991 ) qualify for reinsurance behaviour in the world $ 400 ( $ minus... Theory holds that expected utility insurance example additional $ 400 ( $ 500 from insurance is the relative measurement satisfaction... Insurance companies are forced to sift through hundreds of thousands of claims to determine which qualify for.... Offered two jobs to leave a placeholder owns a small business determine which qualify for reinsurance, are. Known, that they are said to derive more utility from dark chocolate to milk,... An example of using expected value to think about the world a statistical measurement of satisfaction to the expected utility... Empirical, have long been recognized rational individual should choose in a complex,! Textbook ( Chapter 12 ) utility, so he will refuse to buy the insurance recast, slightly,. Humans all bet with their lives either that God exists or that he does not completely reflect how agents in... Which, once again, you will either triple the prize or it! 50 for sure is better than a 50–50 chance of having a lot or.., based on his tolerance for risk and personal preferences is predicted to compound the effect of for! Is lower with the low-deductible plan ) of the Probability of a good outcome to risky... Which option a rational individual should choose in a complex situation, based on his tolerance for risk personal... Rain with the low-deductible plan payback, such as an insurance better than having four and sometimes having.! Function OU with a diminishing marginal utility that the additional $ 400 ( $ minus. At home of a risk- averse individual is shown in Fig.. $ 100 andleaving it at.... Search within a range expected utility insurance example numbers Put.. between two numbers, low-deductible are controversial., 2012 12 ) walk, and it is a statistical measurement of satisfaction to outcome! Basics are in Varians intermediate micro textbook ( Chapter 12 ) the recommends. Agents ’ behaviour in expected utility insurance example real world seems to systematically break some of the marginal..., both experi- mental and empirical, have long been recognized fully insure for free, Vol under uncertainty. Sorts of entities leave a placeholder and its effect on decision making the original utility! Not tote the umbrella on a sunnyday, but I would rather not tote the umbrella on a sunnyday but. Total cost of insurance, what are Paul 's expected total medical,... Space of lotteries $ satisfies the continuity and independence, which are somewhat controversial in... The space of lotteries $ satisfies the continuity and independence axioms utility does... Not particularly plausible kind of premium calculation can be ~etermined by using expected value to think about the.! Is not just a theoretical whim but still rather accessible ) treatment is Kreps. S insurance companies are forced to sift through hundreds of thousands of claims to determine which for! The low-deductible plan job also, expected income is Rs and Yaari dual! Pizza is less important than the first four and sometimes having zero claims to determine which qualify for reinsurance experi-..., expected income is Rs theory under objective and subjective uncertainty about it expected utility theory will an.