本书是“精算科学系列”之一，该书将寿险模型建立在不能确定终止日期的一系列现金流上，并结合金融理论和概率分布理论，重点讲述如何对寿险和年金进行定价，是一本寿险理论的概率应用书，它将有助于那些对精算科学有兴趣的读者迅速掌握本领域必备的基础知识。该书可供各大专院校作为教材使用，也可供从事相关工作的人员作为参考用书使用。

精算师是运用精算方法和技术解决经济问题的专业人士，既可是商业保险界的核心精英，又可在金融投资、咨询等众多领域担任要职。目前国内精算人才紧缺，且随着众多外资银行进入中国，中国的精算师的教育变得更加紧迫。这套英文版《精算科学系列》将有助于那些对精算科学有兴趣的读者迅速掌握本领域必备的基础知识。

本书将寿险模型建立在不能确定终止日期的一系列现金流上，并结合金融理论和概率分布理论，重点讲述如何对寿险和年金进行定价，是一本寿险理论的概率应用书。

本书意在帮助有兴趣于精算学和寿险理论的读者理解寿险理论的定价体系。由于本书中众多例子及练习取自往年北美精算师(SOA)考试试题，使得本书也是一本针对北美精算师Exam MLC及英国精算师Subject CT5的很好的参考书。

Preface

1 Interest and Annuity-Certain

 1.1 Introduction

 1.2 Interest

1.2.1 Simple Interest

1.2.2 Compound Interest

1.2.3 Interest Convertible m-thly

1.2.4 Force cf Interest

1.2.5 Relationship among Interest Rates

1.2.6 The Accumulation Factor

1.2.7 The Discount Factor

 1.3 Annuities-Certain

1.3.1 Annual Annuities-Certain

1.3.2 Continuous Annuities-Certain

1.3.3 m-thly Annuities-Certain

1.3.4 Accumulated Values of Annuities-Certain at Time n

 1.4 Summary

 1.5 Exercise

2 Individual Future Lifetime

 2.1 Introduction

 2.2 A Newborn's Future Lifetime X

 2.3 Future Lifetime of (x)

2.3.1 Relationship Between Probability Functions of X and T(x)

2.3.2 Curtate-Future-Lifetime of (x)

2.3.3 Conditional Average Death Time

2.3.4 Central Force of Mortality

 2.4 Life Table

2.4.1 Aggregate Life Table

2.4.2 Select-and-Ultimate Life Table

 2.5 Summary

 2.6 Exercise

3 Life Insurance

 3.1 Introduction

 3.2 Continuous Life Insurance

3.2.1 Level Life Insurance

3.2.2 A General Continuous Life Insurance

 3.3 Discrete Life Insurance

3.3.1 Level Life Insurance

3.3.2 A General Discrete Life Insurance

3.3.3 Commutation Functions

 3.4 m-thly Life Insurance

 3.5 Endowment Insurance

 3.6 Summary

 3.7 Exercise

4 Life Annuities

 4.1 Introduction

 4.2 Continuous Life Annuities

4.2.1 Level Life Annuities

4.2.2 Varying Continuous Life Annuities

 4.3 Annual Life Annuities

4.3.1 Level Annual Life Annuities

4.3.2 Varying Annual Life Annuities

4.3.3 Commutation Functions

 4.4 Special Life Annuities

4.4.1 m-thly Life Annuities

4.4.2 n-Year-Certain-and-Life Annuities

4.4.3 Apportionable Annuities-Due

4.4.4 Complete Annuities-immediate

 4.5 Summary

 4.6 Exercise

5 Insurance Premiums

 5.1 Introduction

 5.2 Insurance Pricing Principles

5.2.1 The Three Pricing Principles

5.2.2 Single Benefit Premiums

 5.3 Benefit Premiums

5.3.1 Fully Continuous Benefit Premiums

5.3.2 Fully Discrete Benefit Premiums

5.3.3 m-thly Benefit Premiums

5.3.4 Apportionable Benefit Premiums

 5.4 Gross Insurance Premiums

5.4.1 Classification of Expenses

5.4.2 Gross Premiums Under the Equivalence Principle

 5.5 Summary

 5.6 Exercises

6 Insurance Reserves

 6.1 Introduction

 6.2 Insurance Reserve Principles

6.2.1 The Prospective Loss Random Variable

6.2.2 The Three Common Principles

 6.3 Insurance Benefit Reserves

6.3.1 Benefit Reserves for Fully Continuous Life Insurance

6.3.2 Benefit Reserves for Fully Discrete Life Insurance

6.3.3 Benefit Reserves with the Retrospective Method

6.3.4 Recursive Formula between Discrete Benefit Reserves

 6.4 Benefit Reserves for Special Life Insurance

6.4.1 Benefit Reserves for m-thiy Life Insurance

6.4.2 Benefit Reserves for Mixed Life Insurance

6.4.3 Benefit Reserves with Apportionable Premiums

6.4.4 Gross Insurance Reserves

 6.5 Summary

 6.6 Excercise

7 Joint-Life Functions

 7.1 Introduction

 7.2 Joint Distributions of Future Lifetimes

7.2.1 The Joint-Life Status

7.2.2 Last-Survivor Status (■)

 7.3 Relationship among T(x), T(y), Txy,and T■

 7.4 Contingent Probabilities

 7.5 Dependent Models

7.5.1 Common Shock Model

7.5.2 Frank's Copula

 7.6 Life Insurance on Two Individuals

7.6.1 Life Insurance on (xy) and (■)

7.6.2 Contingent Life Insurance

 7.7 Life Annuities on Two Individuals

7.7.1 Life Annuities on (xy) and (■)

7.7.2 Reversionary Annuities

 7.8 Summary

 7.9 Exercise

8 Multiple-Decrement Model

 8.1 Introduction

 8.2 A Double-Decrement Model

8.2.1 Future Lifetimes of Two Risks

8.2.2 Probabilities of Decrement

 8.3 A General m-Decrement Model

8.3.1 Probabilities of Decrement

8.3.2 Central Rates from a Multiple-Decrement Table

8.3.3 Constructing a Multiple-Decrement Table

 8.4 Discretionary Life Insurance

8.4.1 Benefit Premiums for Discretionary Life Insurance

8.4.2 Benefit Reserves for Discretionary Life Insurance

8.4.3 Asset Share

 8.5 Summary

 8.6 Exercise

Appendix 1 Standard Normal Table

Appendix 2A Illustrative Life Table with i＝0.06

Appendix 2B Illustrative Service Table with i＝0.06

Appendix 2C Interest Rate Function at i＝0.06

Appendix 3 Probability Theorem and Random Variables

Appendix 4 Interest Rate and Annuity-Certain

Bibliography

Symbol Index

Index