Prospect Theory: For Risk and Ambiguity

Half-title......Page 3
Title......Page 5
Copyright......Page 6
Contents......Page 7
Preface......Page 15
Introduction\n......Page 17
Behavioral foundations......Page 18
Intended audience......Page 19
Structure......Page 20
Preview......Page 21
Our five-step presentation of decision models......Page 23
Part I Expected utility......Page 25
Examples of decision making under uncertainty......Page 27
1.2 Basic properties of preferences......Page 31
1.3 Expected value......Page 33
1.4 Data fitting for expected value......Page 35
1.5 The bookmaking argument of de Finetti, or the no-arbitrage condition from finance......Page 38
1.6 A behavioral foundation of subjective probabilities and expected value using no-arbitrage and no-book......Page 43
1.7 Discussion of Structural Assumption 1.2.1 (Decision under uncertainty)......Page 48
1.8 The general nature and usefulness of behavioral foundations......Page 50
Appendix 1.9 Natural, technical, and intuitive preference conditions, and the problematic completeness condition......Page 53
Appendix 1.10 The relation of Theorem 1.6.1 to the literature......Page 55
Appendix 1.11 Proof of Theorem 1.6.1 and Observation 1.6.1......Page 57
2.1 Decision under risk as a special case of decision under uncertainty......Page 60
2.2 Decision under risk: basic concepts......Page 63
2.3 Decision under risk as a special case of decision under uncertainty; continued......Page 64
2.4 Choices under risk and decision trees......Page 67
2.5 Expected utility and utility measurement......Page 69
2.6 Consistency of measurement and a behavioral foundation of expected utility......Page 73
2.7 Independence and other preference conditions for expected utility......Page 79
2.8 Basic choice inconsistencies......Page 81
Appendix 2.9 Proof of Theorem 2.6.3 and Observation 2.6.3......Page 83
3.1 An application from the health domain: decision tree analysis......Page 85
3.2 Risk aversion......Page 87
3.3 Applications of risk aversion......Page 90
3.4 Indexes of risk aversion......Page 93
3.5 Parametric families of utility......Page 94
Empirical meaning of risk tolerance......Page 98
3.6 Data fitting for expected utility under risk......Page 99
3.7 Multiattribute utility......Page 101
3.8 Taxation and welfare theory with cardinal utility......Page 107
3.9 Proofs for Chapter 3......Page 108
4.1 Fifteen preference questions......Page 110
4.2 (Subjective) expected utility......Page 116
4.3 Measuring utility and testing EU for §4.1......Page 119
4.4 A decision process......Page 123
4.5 General utility measurement and the tradeoff notation......Page 124
4.6 A behavioral foundation of expected utility......Page 126
4.7 Further discussion of Theorem 4.6.4 (Uncertainty-EU)......Page 128
4.8.1 Savage\'s sure-thing principle......Page 130
4.8.2 Utility analysis based on t-indifferences......Page 131
4.8.3 Debreu\'s additive decomposability and state-dependent utility......Page 133
4.9 A hybrid case: subjective probabilities and utilities when also objective probabilities are given......Page 134
4.9.1 A general (\"single-stage\") approach......Page 135
4.9.2 A behavioral foundation for the single-stage approach......Page 136
4.9.3 The multi-stage approach of Anscombe and Aumann (1963)......Page 138
4.9.4 Comparing the Anscombe and Aumann model with the single-stage approach......Page 141
4.10 Data fitting for expected utility under uncertainty......Page 143
4.11 A statistical analysis of the experiment of §4.1, revealing violations of expected utility......Page 147
4.12 The Allais paradox: a well-known violation of expected utility......Page 149
Appendix 4.13 Experimental economics\' real-incentive principle and the tradeoff method......Page 151
Appendix 4.14 Tradeoff consistency as a generalization of de Finetti\'s bookmaking......Page 154
Appendix 4.15 Proofs for Chapter 4......Page 155
Part II Nonexpected utility for risk......Page 159
5.1 Probabilistic sensitivity versus outcome sensitivity for single-nonzero-outcome-prospects......Page 161
5.2 Probabilistic sensitivity for multi-outcome prospects, and the old way of transforming probabilities......Page 165
5.3 A violation of stochastic dominance......Page 169
5.4 Rank-dependent utility: discovering the formula using psychological intuition......Page 171
5.5 Rank-dependent utility: discovering the formula using mathematical intuition......Page 177
5.6 Calculating rank-dependent utility......Page 181
5.7 Conclusion......Page 184
6.1 Ranks, ranked probabilities, and rank-dependent utility defined......Page 185
6.3 Where rank-dependent utility deviates from expected utility: optimism and pessimism......Page 188
6.4.1 The certainty effect......Page 192
6.4.2 Further discussion of rank dependence......Page 194
6.5.1 Measuring utility under rank-dependent utility......Page 197
6.5.2 A behavioral foundation of rank-dependent utility......Page 200
6.5.3 An elaborated example......Page 201
6.5.5 Further implications of rank-dependent utility......Page 204
Appendix 6.6 Yet further deviations of rank-dependent utility from expected utility......Page 206
Appendix 6.7 Ranking identical outcomes and collapsing outcomes......Page 210
Appendix 6.8 An interpretation of rank-dependent utility using the derivative of w......Page 213
Appendix 6.9 RDU for continuous distributions and figures for negative outcomes......Page 215
7.1 Likelihood insensitivity and pessimism as two components of probabilistic risk attitudes......Page 219
7.2 Parametric forms of weighting functions......Page 222
7.3 Data fitting for rank-dependent utility under risk......Page 227
7.4 Direct ways to test convexity, concavity, and likelihood insensitivity using violations of the sure-thing principle......Page 230
7.5 An alternative direct way to directly investigate properties of nonlinear decision weights......Page 233
7.6 Bad-news probabilities or loss-ranks......Page 235
7.7 A formal definition of likelihood insensitivity (inverse-S)......Page 238
7.8 The choice of insensitivity region......Page 242
7.9 Discussion of likelihood insensitivity......Page 243
7.10 Indexes of pessimism and likelihood insensitivity......Page 245
7.11 Binary rank-dependent utility......Page 246
Appendix 7.12 Alternative definition of likelihood insensitivity: first concave and then convex......Page 247
Appendix 7.13 Proofs for Chapter 7......Page 249
8 Where prospect theory deviates from rank-dependent utility and expected utility: reference dependence versus asset integration......Page 250
8.1 A choice paradox......Page 251
8.2 A discussion and the real culprit of the paradox......Page 252
8.3 Deviations from a fixed reference point (\"initial wealth\"\n) as nothing but an alternative way of modeling final wealth, and of incorporating some empirical improvements......Page 253
8.4 Loss aversion defined......Page 254
8.5 Deviations from a variable reference point as a major breakaway from final-wealth models......Page 256
8.6 Rabin\'s paradox......Page 258
8.7 Future directions for theories of reference dependence......Page 261
Appendix 8.8 Empirical meaningfulness problems of loss aversion......Page 263
Appendix 8.9 A formal model of initial wealth and reference points......Page 265
9.1 A symmetry about 0 underlying prospect theory......Page 267
9.2 The definition of prospect theory......Page 268
9.3 Properties of the prospect theory formula, and calculations......Page 270
9.4.1 Monotonicity, stochastic dominance, and the sure-thing principle......Page 276
9.4.2 Measuring utility, event weighting, and loss aversion......Page 278
9.5 Empirical findings on prospect theory......Page 280
9.6.1 The first problem: loss aversion depends on the monetary unit......Page 283
9.6.2 The second problem: always U(α)-U(-α) for some outcome α> 0......Page 286
Appendix 9.7 Some theoretical issues concerning prospect theory......Page 287
Appendix 9.8 Original prospect theory of 1979......Page 289
Part III Nonexpected utility for uncertainty......Page 293
10.1 Probabilistic sophistication......Page 295
10.2 Rank-dependent utility defined for uncertainty and without probabilistic sophistication......Page 298
10.3.1 Ellsberg\'s violation of probabilistic sophistication......Page 302
10.3.2 Further observations......Page 303
10.4 Where rank-dependent utility under uncertainty deviates from expected utility in the same way as it did under risk......Page 304
10.4.1 Optimism and pessimism......Page 305
10.4.2 Likelihood insensitivity (Inverse-S)......Page 306
10.4.3 Direct ways to test convexity, concavity, and likelihood insensitivity using violations of the sure-thing principle......Page 308
10.5.1 Rank-preference conditions......Page 310
10.5.2 Measuring utility (and event weighting) under RDU......Page 311
10.5.3 A behavioral foundation for RDU......Page 313
10.6 Binary rank-dependent utility......Page 314
10.7.1 A general (\"single-stage\") approach......Page 315
10.7.2 A behavioral foundation for the single-stage approach......Page 316
10.7.3 Schmeidler\'s and Jaffray\'s two-stage approaches......Page 317
10.8 Bad-news events or loss-ranks......Page 320
10.9 Further observations regarding rank dependence......Page 321
Appendix 10.10 An integral representation......Page 325
Appendix 10.13 Proofs for Chapter 10......Page 326
Appendix 10.14 Proof of Theorem 6.5.6......Page 332
11.1 The Ellsberg paradox and the home bias as within-subject between-source comparisons......Page 333
11.2 Using rank dependence to analyze ambiguity......Page 334
11.3 Elaborated examples for ranks, ambiguity premiums, and hedging in finance......Page 338
11.4 The CORE......Page 339
11.5 Multiple priors (Maxmin expected utility and α-maxmin): basic results......Page 340
11.6 Approaches in the literature that we will not take......Page 343
11.7 Indexes of ambiguity aversion......Page 344
11.8 Indexes of ambiguity aversion and sensitivity......Page 348
Appendix 11.9 Discussion of multiple priors and other models......Page 351
Appendix 11.10 Violations of monotonicity for multiple priors......Page 354
Appendix 11.11 Mobius transforms and belief functions......Page 355
12.1 Prospect theory defined......Page 358
12.3.1 Sign-preference conditions......Page 360
12.3.2 Measuring utility (and event weighting) under prospect theory......Page 361
12.3.3 Measuring loss aversion under prospect theory......Page 362
12.3.4 A behavioral foundation for prospect theory......Page 363
12.5 Loss aversion versus ambiguity aversion......Page 365
12.6 Violations of prospect theory and rank dependence......Page 366
12.7 Indexes of ambiguity attitudes under prospect theory......Page 370
Appendix 12.8 Some theoretical issues concerning prospect theory for uncertainty......Page 372
Appendix 12.9 Proofs for Chapter 12......Page 373
13 Conclusion......Page 374
A.1 Nonparametric measurements and parametric fittings for imperfect models: general discussion......Page 375
A.2 Our distance measure for parametric fitting......Page 377
A.3 Discussion of the distance measure......Page 379
Appendix B: Choosing from multiple prospects and binary choice: the principles of revealed preference\n......Page 382
B.1 Examples......Page 383
B.2 A behavioral foundation of preference relations derived from choice behavior......Page 387
B.3 Assumptions underlying revealed preference......Page 390
B.4 The history of revealed preference......Page 394
Appendix C: Dynamic decisions\n......Page 396
Appendix D: Applications other than decision under uncertainty......Page 400
Appendix E: Bisymmetry-based preference conditions......Page 403
Appendix F: Nonmonotonic rank-dependent models and the Fehr-Schmidt model of welfare evaluation......Page 407
Appendix G: Extensions of finite-dimensional results to infinite-dimensional results: a meta-theorem......Page 409
Appendix H: Measure theory......Page 411
Appendix I: Related textbooks and surveys......Page 413
Appendix J: Elaborations of exercises......Page 415
Appendix K: Skipping parts and interdependencies between sections......Page 471
References......Page 477
Author index......Page 508
Subject index......Page 516