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The Economic Theory of Annuities
Eytan Sheshinski

Book Description | Endorsements
Chapter 1 [HTML] or [PDF format]

TABLE OF CONTENTS:

Preface xiii

Chapter 1: Introduction 1
1.1 Brief Outline of the Book 5
1.2 Short History of Annuity Markets 9
1.3 References to Actuarial Finance 11
Chapter 2: Benchmark Calculations: Savings and Retirement 12
Chapter 3: Survival Functions, Stochastic Dominance, and Changes in Longevity 15
3.1 Survival Functions 15
3.2 Changes in Longevity 18

Chapter 4: Life Cycle Model with Longevity Risk: First Best and Competitive Equilibrium 21
4.1 First Best 21
4.2 Competitive Equilibrium: Full Annuitization 23
4.3 Example: Exponential Survival Function 25
4.4 Equivalence of Short-term, Long-term, and Deferred Annuities 26
Appendix 27

Chapter 5: Comparative Statics, Discounting, Partial Annuitization, and No Annuities 29
5.1 Increase in Wages 29
5.2 Increase in Longevity 30
5.3 Positive Time Preference and Rate of Interest 32
5.4 Partial Annuitization: No Short-term Annuity Market 33
5.5 Partial Annuitization: Low Returns on Annuities 35
5.6 Length of Life and Retirement 35
5.7 Optimum Without Annuities 38
5.8 No Annuities: Risk Pooling by Couples 40
5.9 Welfare Value of an Annuity Market 41
5.10 Example: Exponential Survival Function 42
Appendix 44

Chapter 6: Subjective Beliefs and Survival Probabilities 45
6.1 Deviations of Subjective from Observed Frequencies 45
6.2 Behavioral Effects 45
6.3 Exponential Example 47
6.4 Present and Future Selves 48

Chapter 7: Moral Hazard 51
7.1 Introduction 51
7.2 Comparison of First Best and Competitive Equilibrium 51
7.3 Annuity Prices Depending on Medical Care 54
Appendix 55

Chapter 8: Uncertain Future Survival Functions 56
8.1 First Best 56
8.2 Competitive Separating Equilibrium (Risk-class Pricing) 59
8.3 Equilibrium with Short-term Annuities 60
8.4 The Efficiency of Equilibrium with Long-term Annuities 62
8.5 Example: Exponential Survival Functions 65

Chapter 9: Pooling Equilibrium and Adverse Selection 67
9.1 Introduction 67
9.2 General Model 69
9.3 Example 71
Appendix 75

Chapter 10: Income Uncertainty 77
10.1 First Best 77
10.2 Competitive Equilibrium 78
10.3 Moral Hazard 79

Chapter 11: Life Insurance and Differentiated Annuities 81
11.1 Bequests and Annuities 81
11.2 First Best 83
11.3 Separating Equilibrium 84
11.4 Pooling Equilibrium 84
11.5 Period-certain Annuities and Life Insurance 87
11.6 Mixed Pooling Equilibrium 90
11.7 Summary 93
Appendix 94

Chapter 12: Annuities, Longevity, and Aggregate Savings 97
12.1 Changes in Longevity and Aggregate Savings 97
12.2 Longevity and Individual Savings 98
12.3 Longevity and Aggregate Savings 98
12.4 Example: Exponential Survival Function 102
12.5 No Annuities 103
12.6 Unintended Bequests 104
Appendix 106

Chapter 13: Utilitarian Pricing of Annuities 109
13.1 First-best Allocation 109
13.2 Competitive Annuity Market with Full Information 112
13.3 Second-best Optimum Pricing of Annuities 113
Appendix 116

Chapter 14: Optimum Taxation in Pooling Equilibria 118
14.1 Introduction 118
14.2 Equilibrium with Asymmetric Information 119
14.3 Optimum Commodity Taxation 122
14.4 Optimum Taxation of Annuities 125
Appendix 129

Chapter 15: Bundling of Annuities and Other Insurance Products 131
15.1 Introduction 131
15.2 Example 132

Chapter 16: Financial Innovation--Refundable Annuities (Annuity Options) 135
16.1 The Timing of Annuity Purchases 135
16.2 Sequential Annuity Market Equilibrium Under Survival Uncertainty 137
16.3 Uncertain Future Incomes: Existence of a Separating Equilibrium 140
16.4 Refundable Annuities 144
16.5 A Portfolio of Refundable Annuities 146
16.6 Equivalence of Refundable Annuities and Annuity Options 147
Appendix 150

References 153
Index 157

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File created: 4/17/2014

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