Economic Theory of Annuities

Preface xiii Introduction 1(11) Brief Outline of the Book 5(4) Short History of Annuity Markets 9(2) References to Actuarial Finance 11(1) Benchmark Calculations: Savings and Retirement 12(3) Survival Functions, Stochastic Dominance, and Changes in Longevity 15(6) Survival Functions 15(3) Changes in Longevity 18(3) Life Cycle Model with Longevity Risk: First Best and Competitive Equilibrium 21(8) First Best 21(2) Competitive Equilibrium: Full Annuitization 23(2) Example: Exponential Survival Function 25(1) Equivalence of Short-term, Long-term, and Deferred Annuities 26(3) Appendix 27(2) Comparative Statics, Discounting, Partial Annuitization, and No Annuities 29(16) Increase in Wages 29(1) Increase in Longevity 30(2) Positive Time Preference and Rate of Interest 32(1) Partial Annuitization: No Short-term Annuity Market 33(2) Partial Annuitization: Low Returns on Annuities 35(1) Length of Life and Retirement 35(3) Optimum Without Annuities 38(2) No Annuities: Risk Pooling by Couples 40(1) Welfare Value of an Annuity Market 41(1) Example: Exponential Survival Function 42(3) Appendix 44(1) Subjective Beliefs and Survival Probabilities 45(6) Deviations of Subjective from Observed Frequencies 45(1) Behavioral Effects 45(2) Exponential Example 47(1) Present and Future Selves 48(3) Moral Hazard 51(5) Introduction 51(1) Comparison of First Best and Competitive Equilibrium 51(3) Annuity Prices Depending on Medical Care 54(2) Appendix 55(1) Uncertain Future Survival Functions 56(11) First Best 56(3) Competitive Separating Equilibrium (Risk-class Pricing) 59(1) Equilibrium with Short-term Annuities 60(2) The Efficiency of Equilibrium with Long-term Annuities 62(3) Example: Exponential Survival Functions 65(2) Pooling Equilibrium and Adverse Selection 67(10) Introduction 67(2) General Model 69(2) Example 71(6) Appendix 75(2) Income Uncertainty 77(4) First Best 77(1) Competitive Equilibrium 78(1) Moral Hazard 79(2) Life Insurance and Differentiated Annuities 81(16) Bequests and Annuities 81(2) First Best 83(1) Separating Equilibrium 84(1) Pooling Equilibrium 84(3) Period-certain Annuities and Life Insurance 87(3) Mixed Pooling Equilibrium 90(3) Summary 93(4) Appendix 94(3) Annuities, Longevity, and Aggregate Savings 97(12) Changes in Longevity and Aggregate Savings 97(1) Longevity and Individual Savings 98(1) Longevity and Aggregate Savings 98(4) Example: Exponential Survival Function 102(1) No Annuities 103(1) Unintended Bequests 104(5) Appendix 106(3) Utilitarian Pricing of Annuities 109(9) First-best Allocation 109(3) Competitive Annuity Market with Full Information 112(1) Second-best Optimum Pricing of Annuities 113(5) Appendix 116(2) Optimum Taxation in Pooling Equilibria 118(13) Introduction 118(1) Equilibrium with Asymmetric Information 119(3) Optimum Commodity Taxation 122(3) Optimum Taxation of Annuities 125(6) Appendix 129(2) Bundling of Annuities and Other Insurance Products 131(4) Introduction 131(1) Example 132(3) Financial Innovation---Refundable Annuities (Annuity Options) 135(18) The Timing of Annuity Purchases 135(2) Sequential Annuity Market Equilibrium Under Survival Uncertainty 137(3) Uncertain Future Incomes: Existence of a Separating Equilibrium 140(4) Refundable Annuities 144(2) A Portfolio of Refundable Annuities 146(1) Equivalence of Refundable Annuities and Annuity Options 147(6) Appendix 150(3) References 153(4) Index 157