Eytan Sheshinski is the Sir Isaac Wolfson Professor of Public Finance at Hebrew University. He is the coeditor of "Entrepreneurship, Innovation, and the Growth Mechanism of the Free-Enterprise Economies" (Princeton) and "Optimal Pricing, Inflation, and the Cost of Price Adjustment".

"Eytan Sheshinski has written the definitive book on the economics of annuities. In light of the demographic transitions in many countries and the changing nature of social insurance, this work will be extremely important in the years ahead."—Jerry R. Green, Harvard University

• 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

Eytan Sheshinski is the Sir Isaac Wolfson Professor of Public Finance at Hebrew University. He is the coeditor of "Entrepreneurship, Innovation, and the Growth Mechanism of the Free-Enterprise Economies" (Princeton) and "Optimal Pricing, Inflation, and the Cost of Price Adjustment".

"Eytan Sheshinski has written the definitive book on the economics of annuities. In light of the demographic transitions in many countries and the changing nature of social insurance, this work will be extremely important in the years ahead."—Jerry R. Green, Harvard University

• 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

Eytan Sheshinski is the Sir Isaac Wolfson Professor of Public Finance at Hebrew University. He is the coeditor of "Entrepreneurship, Innovation, and the Growth Mechanism of the Free-Enterprise Economies" (Princeton) and "Optimal Pricing, Inflation, and the Cost of Price Adjustment".

"Eytan Sheshinski has written the definitive book on the economics of annuities. In light of the demographic transitions in many countries and the changing nature of social insurance, this work will be extremely important in the years ahead."—Jerry R. Green, Harvard University

• 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