expected utility theory, pdf

0000475748 00000 n 1135 0 obj <>stream 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. 0000002905 00000 n London, Edward Elgar, 1997, p. 342-350). 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Ideal events are events Esuch that Savage’s sure thing principle holds for Eand Ec. ˘ ˇ ˆ ˙ ˝˛ 2 ˚=˙ ˚ C F J 455 ˚ Created Date: 10/8/2001 12:06:06 PM 0000003163 00000 n EU DP i n = i i … According to standard decision theory, when … %PDF-1.6 %���� Then % admits a utility representation of the expected utility form. But questions arise when we try to articulate what this kind of modeling amounts to. Expected Utility 4. trailer • Individuals should act in a particular way when they do decision making under the uncertainty. Subjective expected utility theory (Savage, 1954): under assumptions roughly similar to ones form this lecture, preferences have an expected utility representation where both the utilities ��Ʀ b�D�IӮ1��j=j�j&�D����1��ai���������w� B V>0,-�6��� �� This … 0000001244 00000 n 0000004711 00000 n 0000019065 00000 n 9. First, there areoutcomes—object… 0000005019 00000 n 0000004096 00000 n {���\E��:��C7c=�^O�:�*����>-��'d��MZ��H��KN!+`2�v{��B�u�`�(0���/�`O��M�����o�#��x��B��~'�_��/V�~9��D�U#���\ZOD2����7�� ��f2��I��������/���%�� G,��ci�bD�1f�T�.t�S�A���׹&6�$ȡÇ����ίHC����0A&�1��;�!�v O\G�(�W"8a���G,`B. 1090 46 0000006254 00000 n H�b```�o�� ����� �3�xTy���xW��U��{P ���挏���I���ٕߙ�n������U�]:���3��wyd#����E~��a�Y����p�f� � 7n@� p�* �`w�30�s9��"���%�5lz Mean-variance preferences [L4.6] • Excepted utility theory deals with the risk not the uncertainty. 0000009045 00000 n De nition:Full insurance is d = 1. 0000003643 00000 n endstream endobj 83 0 obj 242 endobj 57 0 obj << /Type /Page /Parent 41 0 R /Resources 58 0 R /Contents [ 64 0 R 66 0 R 68 0 R 70 0 R 72 0 R 74 0 R 76 0 R 78 0 R ] /MediaBox [ 0 0 595 842 ] /CropBox [ 0 0 595 842 ] /Rotate 0 >> endobj 58 0 obj << /ProcSet [ /PDF /Text ] /Font << /TT5 60 0 R /TT6 62 0 R >> /ExtGState << /GS1 81 0 R >> >> endobj 59 0 obj << /Type /FontDescriptor /Ascent 822 /CapHeight 692 /Descent -277 /Flags 34 /FontBBox [ -166 -283 1021 927 ] /FontName /OEEALE+Palatino-Roman /ItalicAngle 0 /StemV 84 /XHeight 469 /FontFile2 79 0 R >> endobj 60 0 obj << /Type /Font /Subtype /TrueType /FirstChar 32 /LastChar 233 /Widths [ 250 278 0 0 0 0 0 208 333 333 0 606 250 333 250 606 500 500 500 500 500 500 500 500 500 500 250 250 0 606 0 444 0 778 611 709 774 611 556 763 832 337 333 726 611 946 831 786 604 786 668 525 613 778 722 1000 667 667 0 0 0 0 0 0 0 500 553 444 611 479 333 556 582 291 234 556 291 883 582 546 601 560 395 424 326 603 565 834 516 556 500 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 278 500 500 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 479 479 ] /Encoding /WinAnsiEncoding /BaseFont /OEEALE+Palatino-Roman /FontDescriptor 59 0 R >> endobj 61 0 obj << /Type /FontDescriptor /Ascent 822 /CapHeight 692 /Descent -277 /Flags 98 /FontBBox [ -170 -276 1010 918 ] /FontName /OEEBFM+Palatino-Italic /ItalicAngle -15 /StemV 84 /XHeight 482 /FontFile2 80 0 R >> endobj 62 0 obj << /Type /Font /Subtype /TrueType /FirstChar 32 /LastChar 122 /Widths [ 250 0 0 0 0 0 0 0 333 333 0 0 250 333 250 0 500 500 500 500 500 500 0 500 0 500 0 0 0 0 0 0 0 722 0 667 778 611 556 722 778 333 333 0 556 944 0 0 611 0 667 556 611 778 0 944 0 0 0 0 0 0 0 0 0 444 463 407 500 389 278 500 500 278 0 444 278 778 556 444 500 0 389 389 333 556 500 722 500 500 444 ] /Encoding /WinAnsiEncoding /BaseFont /OEEBFM+Palatino-Italic /FontDescriptor 61 0 R >> endobj 63 0 obj 484 endobj 64 0 obj << /Filter /FlateDecode /Length 63 0 R >> stream Economists often invoke expected-utility theory to explain substantial (observed or posited) risk aversion over stakes where the theory actually predicts virtual risk neutrality. the expected utility theory that predicts an equal increase, of 0.01U(w) in both cases, U being the utility function. h�bbbJg`b```%F�8w4F�|���M B t component of expected utility theory is as old as probability theory itself. Axiomatic expected utility theory has been concerned with identifying axioms in terms of preferences among actions, that are satisfied if and only if one's behavior is consistent with expected utility, thus providing a foundation to the use of the Bayes action. UTILITY THEORY The expected utility/subjective probability model of risk preferences and beliefs has long been the preeminent model of individual choice under conditions of uncer-tainty. 0000475673 00000 n 0000020769 00000 n His expected utility from buying d dollars of insurance is EU(d) = (1 p)u(w qd) + pu w qd (1 d): Under what conditions will he insure, and for how much of the loss? DEFINITION:AneventE is ideal if [fEh gEhand hEf hEg] implies 0000005481 00000 n 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. H��W�n7�>�>,5�;� @|i� �ZE��Pm�Q���Q;_�CrW�dYC�%)r��r���m'W��V�z58:Z܋O*h��&�����f,F��V�~}tr,Ŀ���k%�g&'�4����� ����h�oo���"KΠ������f*�ů+ؚ�t�m�v���$�&����vn�)'u �1 ��k.#UF xref 0000006683 00000 n Expected utility and the independence axiom A simple exposition of the main ideas Kjell Arne Brekke August 30, 2017 1 Introduction Expected utility is a theory on how we choose between lotteries. The expected utility theory deals with the analysis of situations where individuals must make a decision without knowing which outcomes may result from that decision, this is, decision making under uncertainty.These individuals will choose the act that will result in the highest expected utility, being this the sum of the products of probability and utility over all possible outcomes. 3 Axiomatic Foundations. Expected Utility Expected Utility Theory is the workhorse model of choice under risk Unfortunately, it is another model which has something unobservable The utility of every possible outcome of a lottery So we have to –gure out how to test it We have already gone through this process for the model of ™standard™(i.e. 0000006397 00000 n 0000007728 00000 n 0000002482 00000 n 0000003942 00000 n 6.In the case of \(\rho =\infty \), restricting our attention to the set of measurable pure alternatives, Sect. Prospect Theory Versus Expected Utility Theory: Assumptions, Predictions, Intuition and Modelling of Risk Attitudes Michał Lewandowski∗ Submitted: 3.04.2017,Accepted: 4.12.2017 Abstract The main focus of this tutorial/review is on presenting Prospect Theory in the context of the still ongoing debate between the behavioral (mainly EXPECTED UNCERTAIN UTILITY THEORY 3 For any fg ∈F and A⊂Ω,letfAgdenote the act that agrees with f on Aand with gon the Ac, the complement of A; that is, fAgis the unique act hsuch that A⊂{h=f} and Ac ⊂{h=g}. 55 0 obj << /Linearized 1 /O 57 /H [ 1014 355 ] /L 117387 /E 55875 /N 11 /T 116169 >> endobj xref 55 29 0000000016 00000 n 0000000927 00000 n 0000001369 00000 n 0000001576 00000 n 0000001692 00000 n 0000001922 00000 n 0000002681 00000 n 0000002914 00000 n 0000003397 00000 n 0000003418 00000 n 0000003980 00000 n 0000004001 00000 n 0000004709 00000 n 0000004730 00000 n 0000005566 00000 n 0000005587 00000 n 0000006433 00000 n 0000006454 00000 n 0000007336 00000 n 0000007357 00000 n 0000008188 00000 n 0000008209 00000 n 0000009071 00000 n 0000009092 00000 n 0000009733 00000 n 0000034215 00000 n 0000055585 00000 n 0000001014 00000 n 0000001348 00000 n trailer << /Size 84 /Info 54 0 R /Root 56 0 R /Prev 116159 /ID[] >> startxref 0 %%EOF 56 0 obj << /Type /Catalog /Pages 42 0 R /JT 53 0 R /PageLabels 40 0 R >> endobj 82 0 obj << /S 206 /L 297 /Filter /FlateDecode /Length 83 0 R >> stream So far, probabilities are objective. • Expected utility theory adds to this preferences over uncertain combinations of bundles where uncertainty means that these bundles will be available with known probabilities that are less than unity. Uncertainty/ambiguity aversion 6. ��Qpi�#�p�T�e��F� v^m\0�2�Wo��Υ��P:r�B����ef�[�q�(�Z�s�0�� ��%��9��L�PyFDm��d�[q>ͰT1��D9�f���R�B4q���h�n;�y�Z����V+4qZ~�2}�����T�k���Nwj�������z�ՐP�t�TЙf�i}��Q�������`ݣ�6M_�͛��$�|�4~�|Oӗ Remarkably, they viewed the development of the expected utility model Expected Utility theory • Developed by Von Neuman and Morgenstern in 1944 (VNM) • It is Normative theory of behavior which means it describes how people should rationally behave. Finally, we show that for lotteries characterized by substantial stakes non-expected utility theories fit the data equally well as expected utility theory. 0000009090 00000 n It exhibits a tremendous flexibility in representing aspects of attitudes toward risk, has a well-developed ana- startxref Expected Utility Theory or Risk-Weighted Expected Utility Theory, have been used to model the considerations that govern rational behavior. This informal problem description can be recast, slightly moreformally, in terms of three sorts of entities. 0000006099 00000 n �HΒq�J���_���h=+Jpd8�Π��I�e4�N�D�D�f�a�K�j��"H ����b������d[� Tg�=:�f�PE����3��$��O�&,b�l�! Which of these acts should I choose? (Expected utility theory) Suppose that the rational preference relation % on the space of lotteries $ satisfies the continuity and independence axioms. pÑv�õpá�������hΡ����V�wh� h��� E�^�z��8�rn+�>���m�>�^��#���r�^n/���^�_�^N�s���r��Ћ#\����rLL���&�I\�R��&�4N8��/���` _%c� The concept of expected utility is best illustrated byexample. endstream endobj 1122 0 obj <>stream Risk aversion coefficients and portfolio choice [DD5,L4] 5. Generalized Expected Utility Theory: The Rank-dependent Model JEL Classification codes: D81, C99 0000005790 00000 n An Introduction to Utility Theory 115 The most common technique is to multiply the utility score by the probability of each possible outcome and sum up these weighted scores. Starmer: Developments in Non-Expected Utility Theory 333 Identifying a "best theory" naturally re- quires judgements about the relative importance of predictive accuracy, sim- plicity, tractability, and so on. 0000004865 00000 n <]/Prev 747941/XRefStm 2482>> 0000473852 00000 n 0000005329 00000 n Prudence coefficient and precautionary savings [DD5] 7. 0000003072 00000 n In expected utility theory under objective uncertainty, or risk, the probabilities are a primitive concept representing the objective uncertainty. Subjective Expected Utility Theory. • Expected utility allows people to compare gambles • Given two gambles, we assume people prefer the situation that generates the greatest expected utility – People maximize expected utility 18 Example • Job A: certain income of $50K • Job B: 50% chance of $10K and 50% chance of $90K • Expected income is the same ($50K) but in one case, This will give you the expected utility of the action. 0000005635 00000 n I would rather not tote the umbrella on a sunnyday, but I would rather face rain with the umbrella than withoutit. �Զ����s8J�gX����l� �Z��'@rpV"��Ȉ�p �(v���Y{�5��R��Q����G���m�o�ƍѽ���W����ϞF����^FOž��^Kg�`v�#S��n���!^�ڡ��f4_�ӏ�mu�sRy�t�?���x�3��ST�ϓ���R��BY��S!F6��q��R�A*SY!_���#I4l��ufPڮ��'y�Y5���O�~��f�DL��e�-Fޮv���$M� ���Y�%:c�7�H/W�^�~�����@پ�W�Y��O)2�~���)~ٍ�NЦ;�T9��q"h���qO'�t�f� ��rg�c��z� =����E!zK�{D�R̺���@��� R�u4i�oYEj��" ���\!�N��E�ۤ Ӌ4kx��(���Q���5�\�&F�hO�d����($�āo ��8mG$���˝/�4eYC�Y]����M"MUR 7�YSe**�_�P+��Y �2g�J���?��N�jZ�~/��x�~�)\���j�g�/��'��H�8���G�d1��^*"��F�=���-���}E�H�,z��0 � De nition:Insurance isactuarially fair,sub-fair, orsuper-fairif the expected net payout per unit, p q, is = 0, <0, or >0, respectively. 3 Decreasing marginal utility The second component — the assumption that marginal utility is a decreasing function — EXPECTED UTILITY THEORY Prepared for the Handbook of Economic Methodology (J.Davis, W.Hands, and U.Maki, eds. 3. vNM expected utility theory a) Intuition [L4] b) Axiomatic foundations [DD3] 4. In reality, uncertainty is usually subjective. This will be discussed in Sect. Outline 1. 0000009177 00000 n Expected utility theory is used as a tool for analyzing situations where individuals must make a decision without knowing which outcomes may … 0000474094 00000 n 0 Our theory enjoys a weak form of the expected utility hypothesis. 0000475711 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.. endstream endobj 1117 0 obj <> endobj 1118 0 obj <> endobj 1119 0 obj [1/hyphen 2/space 3/space] endobj 1120 0 obj <> endobj 1121 0 obj <>stream xڵzy|Sם�9�.ҕe[�%y��Œ�&Y�%Y^eY^06x����b��1J�B�C � �Rq�� %%EOF 0000020717 00000 n The experimental evidence against expected utility theo or unconvincing. NON-EXPECTED UTILITY THEORY Mark J. Machina To appear in The New Palgrave Dictionary of Economics, 2nd Edition edited by Steven N. Durlauf and Lawrence E. Blume, Macmillan (Basingstoke and New York), forthcoming Abstract: Beginning with the … hޜT{0�W?߾����R��]eTh<6�Z��A��Ȧ�c)EE��H����� 0000004404 00000 n Demand for Assets (a) Demand for Stocks (b) Demand for Insurance 1 Probability Theory and Expected. less than the expected value of the gamble • E.g., buying insurance Risk-seeking • You would trade a sure amount for a gamble that has a smaller expected value (but the chance of a larger payout) • E.g., buying lottery tickets H�\�͎�0������� In the second chapter, Expected Utility Theory is thoroughly analysed basing on the original publication of von Neumann and Morgenstern (Von Neumann and Morgenstern, 1953). endstream endobj 1134 0 obj <>/Filter/FlateDecode/Index[732 358]/Length 38/Size 1090/Type/XRef/W[1 2 1]>>stream Such judgments are complicated by the fact that the evidence, much of which de- rives from the experimental paradigm, Economics 326: Expected Utility and the Economics of Uncertainty Ethan Kaplan October 3, 2012. When one modifies the experiments to mi tends to support traditional theory. ���%pB�T���K��9M�����YZ���yp���dB�{�8�`�g @Ш��)�0 ���� per unit. Expected utility (EU) theory remains the dominant approach for modeling risky decision-making and has been considered the major paradigm in decision making since World War II, being used predictively in economics and finance, prescriptively in management science, and descriptively in psychology ().Furthermore, EU is the common economic approach for addressing public policy … 0000019258 00000 n 0000003035 00000 n ��WlZ��D�ʒ�-4*����s �����b,�3ⳳ#���1K���~ ��z8`^���JP���m���.����ʕ� �egٳ�^��*]���F,�� Ȏ��6~b�M@���L3/�f�����_ѻ�zͣ9tEG�!t@�h?��C{���Dh��Q4��P#2J%�̫L#�c�_�o�Rj����u���)Y$#o��� G. 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