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. De nition:Full insurance is d = 1. H�\�͎�0������� 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. 0000008887 00000 n Suppose I am planning a long walk, and need to decide whetherto bring my umbrella. 3.3 Proof of expected utility property Proposition. ) ˝˘ ˇ" ˚7 46! 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. startxref 0000020769 00000 n EU DP i n = i i … 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. endstream endobj 1122 0 obj <>stream 0000002482 00000 n 0000009045 00000 n 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 3. vNM expected utility theory a) Intuition [L4] b) Axiomatic foundations [DD3] 4. 0000003035 00000 n 7 shows that our theory exhibits a form of the classical EU theory. In reality, uncertainty is usually subjective. Probability Theory and Expected Value 2. G. Parmigiani, in International Encyclopedia of the Social & Behavioral Sciences, 2001. The theory recommends which option a rational individual should choose in a complex situation, based on his tolerance for risk and personal preferences.. 2. 0000003942 00000 n 1135 0 obj <>stream xref 0000019065 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. 2 Expected Utility We start by considering the expected utility model, which dates back to Daniel Bernoulli in the 18th century and was formally developed by John von Neumann and Oscar Morgenstern (1944) in their book Theory of Games and Economic Be-havior. 0000019258 00000 n • 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, The theory’s main concern is … 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. In expected utility theory under objective uncertainty, or risk, the probabilities are a primitive concept representing the objective uncertainty. 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 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 • Hence, EU theory is a superstructure that sits atop consumer theory. 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. 0000009090 00000 n I would rather not tote the umbrella on a sunnyday, but I would rather face rain with the umbrella than withoutit. 0000005329 00000 n Slightly longer version than the published one. {���\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. 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 ��t�9}�W�4�� ��C݂7V����յ��(!����Cu*>.a!N#��TH #��guCPeH$F����׺Y�PO�G�ĉJKn����}�Ml�k�[�F�M�7������+#��V�+>>�Z��|��+5����H�D�z�6���?_ ����������N�i�$`w�`�ɰ�|�i0u0pCy�9q�譐���M ��[�=D����a���J�����C�����LO�q�"9?��Qyx��~L������TDɔaE�����H�>3�$-�8�&� �Eĝ � �d)9`�Z4��) �@�@ ����i��%ɖ�m�t5�7�Ͱk�ա_:Ps��^GS@�� 7 /;�9�e���ғu�? 0000005790 00000 n hޜT{0�W?߾����R��]eTh<6�Z��A��Ȧ�c)EE��H����� Markowitz proposes a utility function that explains gambling and insurance De nition:Insurance isactuarially fair,sub-fair, orsuper-fairif the expected net payout per unit, p q, is = 0, <0, or >0, respectively. Uncertainty/ambiguity aversion 6. Subjective Expected Utility Theory. Ideal events are events Esuch that Savage’s sure thing principle holds for Eand Ec. 0000006683 00000 n 0000005635 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? 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. The Saint Petersburg Paradox 3. Finally, we show that for lotteries characterized by substantial stakes non-expected utility theories fit the data equally well as expected utility theory. 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