本書是“精算科學繫列”之一，該書將壽險模型建立在不能確定終止日期的一繫列現金流上，並結合金融理論和概率分布理論，重點講述如何對壽險和年金進行定價，是一本壽險理論的概率應用書，它將有助於那些對精算科學有興趣的讀者迅速掌握本領域**的基礎知識。該書可供各大專院校作為教材使用，也可供從事相關工作的人員作為參考用書使用。

精算師是運用精算方法和技術解決經濟問題的專業人士，既可是商業 保險界的核心精英，又可在金融投資、咨詢等眾多領域擔任要職。目前國 內精算人纔緊缺，且隨著眾多外資銀行進入中國，中國的精算師的教育變 得更加緊迫。這套英文版《精算科學繫列》將有助於那些對精算科學有興 趣的讀者迅速掌握本領域必備的基礎知識。 本書將壽險模型建立在不能確定終止日期的一繫列現金流上，並結合 金融理論和概率分布理論，重點講述如何對壽險和年金進行定價，是一本 壽險理論的概率應用書。 本書意在幫助有興趣於精算學和壽險理論的讀者理解壽險理論的定價 體繫。由於本書中眾多例子及練習取自往年北美精算師(SOA)考試試題，使 得本書也是一本針對北美精算師Exam MLC及英國精算師Subject CT5的很好 的參考書。

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