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The book introduces and develops the basic actuarial models and underlying pricing of life-contingent pension annuities and life insurance from a unique financial perspective. The ideas and techniques are then applied to the real-world problem of generating sustainable retirement income towards the end of the human life-cycle. The role of lifetime income, longevity insurance, and systematic withdrawal plans are investigated in a parsimonious framework. The underlying technology and terminology of the book are based on continuous-time financial economics by merging analytic laws of mortality with the dynamics of equity markets and interest rates. Nonetheless, the book requires a minimal background in mathematics and emphasizes applications and examples more than proofs and theorems. It can serve as an ideal textbook for an applied course on wealth management and retirement planning in addition to being a reference for quantitatively-inclined financial planners.

List of Figures and Tables

Ⅰ　MODELS OF ACTUARIAL FINANCE

　1　Introduction and Motivation

1.1 The Drunk Gambler Problem

1.2 The Demographic Picture

1.3 The Ideal Audience

1.4 Learning Objectives

1.5 Acknowledgments

1.6 Appendix: Drunk Gambler Solution

　2　Modeling the Human Life Cycle

2.1 The Next Sixty Years of Your Life

2.2 Future Value of Savings

2.3 Present Value of Consumption

2.4 Exchange Rate between Savings and Consumptio

2.5 A Neutral Replacement Rate

2.6 Discounted Value of a Life-Cycle Plan

2.7 Real vs. Nominal Planning with Inflation

2.8 Changing Investment Rates over Time

2.9 Further Reading

2.10 Problems

　3　Models of Human Mortality

3.1 Mortality Tables and Rates

3.2 Conditional Probability of Survival

3.3 Remaining Lifetime Random Variable

3.4 Instantaneous Force of Mortality

3.5 The ODE Relationship

3.6 Moments in Your Life

　　3.7 Median vs. Expected Remaining Lifetime

　　3.8 Exponential Law of Mortality

　　3.9 Gompertz-Makeham Law of Mortality

　　3.10 Fitting Discrete Tables to Continuous Laws

　　3.11 General Hazard Rates

　　3.12 Modeling Joint Lifetimes

　　3.13 Period vs. Cohort Tables

　　3.14 Further Reading

　　3.15 Notation

　　3.16 Problems

　　3.17 Technical Note: Incomplete Gamma Function in Excel

　　3.18 Appendix: Normal Distribution and Calculus Refresher

　4　Valuation Models of Deterministic Interest

　　4.l Continuously Compounded Interest Rates?

　　4.2 Discount Factors

　　4.3 How Accurate Is the Rule of 72?

　　4.4 Zero Bonds and Coupon Bonds

　　4.5 Arbitrage: Linking Value and Market Price

　　4.6 Term Structure of Interest Rates

　　4.7 Bonds: Nonflat Term Structure

　　4.8 Bonds: Nonconstant Coupons

　　4.9 Taylor's Approximation

　　4.10 Explicit Values for Duration and Convexity

　　4.11 Numerical Examples of Duration and Convexity

　　4.12 Another Look at Duration and Convexity

　　4.13 Further Reading

　　4.14 Notation

　　4.15 Problems

　5　Models of Risky Financial Investments

　　5.1 Recent Stock Market History

　　5.2 Arithmetic Average Return versus Geometric AverageReturn

　　5.3 A Long-Term Model for Risk

　　5.4 Introducing Brownian Motion

　　5.5 Index Averages and Index Medians

　　5.6 The Probability of Regret

　　5.7 Focusing on the Rate of Change

　　5.8 How to Simulate a Diffusion Process

　　5.9 Asset Allocation and Portfolio Construction

　　5.10 Space-Time Diversification

　　5.11 Further Reading

　　5.12 Notation

　　5.13 Problems

　　……

　6　Models of Pension Life Annuities

7 Models of Life Insurance

8 Models of DB vs.DC Pensions

Ⅱ WEALTH MANAGEMENT:APPLICATIONS AND IMPLECATIONS

9 Sustainable Spending at Retirement

10 Longevity Insurance Revisited

Ⅲ ADVANCED TOPICS

11 Options within Variable Annuities

12 The Utility of Ammuitization

13 Final Words

14 Appendix

Bibliography

Index

Moshe A. Milevsky is Associate Professor of Finance at the Schulich School of Buisness at York University and the Executive Director of the IFID Centre in Toronto, Canada. He was elected as a Fellow of the Fields Institute in 2002. Professor Milevsky is c

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书籍介绍

This 2006 book introduces and develops the basic actuarial models and underlying pricing of life-contingent pension annuities and life insurance from a unique financial perspective. The ideas and techniques are then applied to the real-world problem of generating sustainable retirement income towards the end of the human life-cycle. The role of lifetime income, longevity insurance, and systematic withdrawal plans are investigated in a parsimonious framework. The underlying technology and terminology of the book are based on continuous-time financial economics by merging analytic laws of mortality with the dynamics of equity markets and interest rates. Nonetheless, the book requires a minimal background in mathematics and emphasizes applications and examples more than proofs and theorems. It can serve as an ideal textbook for an applied course on wealth management and retirement planning in addition to being a reference for quantitatively-inclined financial planners.