GENERALIZED EXPECTED UTILITY THEORY- THE RANK-DEPENDENT MODEL
行为经济学的数学基础和核心是什么，截至目前：THE RANK-DEPENDENT MODEL
PARTl
THE EXPECTED UTILITY MODEL

CHAPTER 1
Uncertainty 3
1.1 The Nature of Uncertainty ....................................................................... 3
1.2 Descriptive and Normative Models ............................................................. 4
1.3 Scientific Research Programs ................................................................... 6
CHAPTER 2
Background 7
2.1 EU Theory - History ............................................................................. 7
2.2 EU Theory - An Informal Discussion .......................................................... 9
2.3 Notation — The Discrete Case ................................................................... 10
2.4 Notation - The General Case ................................................................... 13
2.5 Preferences ...................................................................................... 15
CHAPTER 3
EU Theory 17
3.1 The EU Functional .............................................................................. 17
3.2 EU Axioms ....................................................................................... 18
3.3 Risk Aversion in EU Theory ................................................................... 20
3.4 Stochastic Dominance ........................................................................... 2.1
3.5 Risk Preference in EU Theory ........................................................... .......25
3.6 Applications of EU Theory .....................................................................26
3.7 The General Control Problem .................................................................. 28
Concluding Comments .............................................................................. 31
Appendix: ..................................................................' ........................... 33
CHAPTER 4
The Challenge to EU Theory 37
,4-1 The Allais Problem .............................................................................. 37
4.2 The Common Ratio Effect ......................................................................40
4.3 Ambiguity ........................................................................................41
4.4 Preference Reversal .............................................................................43
4.5 Gambling .........................................................................................45
4.6 Insurance ..............................47
4.7 Construction of Utility Functions..............................................................48
4.8 Probability Weighting ...........................................................................49
4.9 Prospect Theory and Subjectively Weighted Utility ........................................ 50


PART 2
THE RANK-DEPENDENT MODEL

CHAPTER 5
Rank-Dependent Expected Utility — An Outline 55
5.1 The Development of RDEU Theory ........................................................... 56
5.2 The RDEU Model ...............................................................................57
5.3 The Transformation Function ..................................................................59
5.4 RDEU -— Probability Weighting Interpretation ..............................................63
5.5 The Dual Approach ..............................................................................65
5.6 The Allais Model................................................................................. 68
5.7 RDEU and Ambiguity...........................................................................70
5.8 RDEU as a Natural Extension..................................................................72
Concluding Comment................................................................................74
CHAPTER 6
Risk Aversion in RDEU Theory 75
6.1 The Correspondence Principle .................................................................76
6.2 Pessimism and RDEU Risk Aversion......................................................... 77
6.3 First and Second Order Risk Aversion........................................................ 80
6.4 Risk Premiums and Coefficients of Risk Aversion .......................................... 82
6.5 An Alternative Definition of Increasing Risk ................................................. 84
6.6 The Rothschild~Stiglitz Theory of Increasing Risk ......................................... 86
6.7 Risk Seeking Behavior..........................................................................88
Concluding Comments ..............................................................................89
CHAPTER 7
Comparative Statics for RDEU Theory 91
7.1 Comparative Static Problems...................................................................91
7.2 Extension Methods ..............................................................................92
7.3 The Extension to RDEU ........................................................................94
7.4 Risk Aversion, Risk Seeking and Comparative Statics .....................................96
7.5 Monotone Spreads and Comparative Risk Aversion .......................................97
7.6 Comparative Risk Aversion in RDEU ........................................................99
Concluding Comments ............................................................................ 100
CHAPTER 8
Risk Seeking and Lottery Design 105
8.1 Lotteries with a Single Prize.................................................................. 106
8.2 The General Case .............................................................................. 109
8.3 Evidence from observed lottery designs .................................................... 111
8.4 Racetrack Betting .............................................................................. 112
Concluding Comments ........................................................................... 1 13

PA RT 3
FURTHER PROPERTIES OF THE MODEL

CHAPTER 9
Some Normative Properties of RDEU 117
9.1 Diversification.................................................................................. 117
9.2 Quasiconcavity, Quasiconvexity and Betweenness ....................................... 120
9.3 Dynamic Consistency ......................................................................... 121
9.4 RDEU and Information ....................................................................... 125
Concluding Comments ............................................................................ 126
CHAPTER 10
RDEU and Experimental Evidence 127
10.1 The Experimental Approach ................................................................ 127
10.2 The Allais Problem .......................................................................... 130
10.3 The Common Ratio Effect .................................................................. 133
10.4 Ambiguity and Reduction of Compound Lotteries ....................................... 134
10.5 Preference Reversal .......................................................................... 135
10.6 The Recent Empirical Evidence on RDEU ................................................ 136
10.7 Estimating a Functional Form .............................................................. 140
CHAPTER 11
Axiomatic Approaches to RDEU 145
11.1 The Probability Weighting Approach ...................................................... 146
11.2 The Dual Approach .......................................................................... 148
11.3 Ordinal Independence and Measure Representation ...................................... 149
11.4 Trade—Off Consistency ...................................................................... 152
11.5 The Reduction of Compound Lotteries Axiom ........................................... 154
11.6 Ordinally Independent Generalizations .................................................... 155
11.7 Cumulative Prospect Theory ................................................................ 157
11.8 The Space of Outcomes ..................................................................... 158
Appendix - Notes on the Original Axiomatization of RDEU .................................. 159

PART 4
GENERALIZED EXPECTED UTILITY THEORY
CHAPTER 12
Generalized Smooth Utility and RDEU 163
12.1 The Model ..................................................................................... 163
12.2 Comparative Statics .......................................................................... 166
12.3 RDEU and Generalized Smooth Preferences ............................................. 168
12.4 Risk Seeking .................................................................................. 169

CHAPTER 13
Stochastic Dominance and Independence Rules 171
13.1 Notation ...........................................................’ ............................ 172
13.2 Dominance Rules............................................................................. 173
13.3 Independence ................................................................................. 176
13.4 Independence in RDEU ..................................................................... 177
13.5 Betweenness Rules .......................................................................... 180
Concluding Comments ............................................................................ 182
CHAPTER 14 .
Extensions 183
14.1 Social Welfare Functions.................................................................... 183
14.2 Constitutional Choice ........................................................................ 185
14.3 Choice over Time ............................................................................ 187
14.4 Time and Uncertainty ........................................................................ 189
14.5 Framing and Coding ......................................................................... 191