Front Matter
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 of 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-thly 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
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
