Life Contingencies
Preface
Acknowledgements
Contributors
For our Readers
1
Introduction
2
Modeling Lifetimes
2.1
Mortality data: Life Expectancies, Deaths, Counts, & Lifetimes
2.1.1
Life Expectancies
2.1.2
Population Mortality Counts
2.1.3
Individual Mortality Data
2.2
Modeling Death
2.2.1
Lifetime Random Variable and its Distribution
2.2.2
Standard Actuarial Notation:
\(q_{\bf{x}}\)
,
\(_tp_{\bf{x}}\)
, and All That
2.2.3
The Classical Case: Age-Only Model
2.3
Analytical Laws of Mortality
2.3.1
De Moivre and Constant Force Models
2.3.2
Gompertz and Makeham Laws
2.3.3
Makeham Law based on Life Expectancies Data
2.4
Life Tables and their Functions
2.4.1
Life Table Basics
2.4.2
Life Table based on U.S. Population Data
2.4.3
Curtate Quantities and Recursive Relationships
2.4.4
Fractional Year Assumptions
2.4.5
Cohort Life Tables and Mortality Improvement Modeling
2.5
Non-parametric Survival Estimation
2.5.1
Kaplan-Meier Estimates
2.5.2
Nelson-Aalen Estimates
2.6
Conditional Models: Survival regression
2.6.1
The Cox Proportional Hazard Model
2.6.2
Cox Models Based on Life Insurer Data
2.6.3
Conditional Life Tables
2.7
Notes and Comments
3
Basic Life Contingent Benefits
3.1
Valuation of Cash Flows under Uncertainty
3.1.1
Moment Calculations
3.1.2
Illustrative Moments of Cash Flows
3.2
Life Insurance Benefits
3.2.1
Whole of life insurance
3.2.2
Term insurance
3.2.3
Pure endowment
3.2.4
Endowment insurance
3.3
Life Annuity Benefits
3.3.1
Life annuity
3.3.2
Term life annuity
3.3.3
Deferred life annuity
3.3.4
Guaranteed life annuity
3.4
Valuing Life Contingent Benefits using a Spreadsheet
3.5
Case Study: A Portfolio of Term Insurance Policies
3.5.1
An individual policy
3.5.2
Moments of a portfolio of policies
3.5.3
Simulated distribution of a portfolio of policies
3.6
Further Resources and Contributors
4
Contingent Payment Techniques
4.1
Contingent Cash Flows Occurring
\(m^{th}\)
ly
4.1.1
Basic Concepts
4.1.2
Illustrative Cash Flows
4.1.3
Contingent Cash Flows in Continuous Time
4.2
Sampling Bias
4.2.1
Population Subsets and Sampling Bias
4.2.2
Sampling Bias in Actuarial Practice
4.3
Using Economics to Motivate Insurance Features
4.3.1
Actuarially Fair Prices and Risk Classification
4.3.2
Selection and Adverse Selection
4.3.3
Asymmetric Information
4.4
Contingent Payment Applications
4.5
Pet Insurance
4.5.1
Introduction to Pet Health Insurance
4.5.2
Canine Mortality
4.5.3
Cost of Care
4.5.4
More on Pet Insurance Markets
4.6
Disability Income Insurance
4.6.1
Introduction to Disability Income Insurance
4.6.2
Disability Recovery Rates
4.6.3
Actuarial Present Values of Disability Income
4.6.4
More on Disability Income Insurance
5
Going Forward
5.1
Table of Contents
5.2
Usage Data
6
Empirical Exercises
6.1
Chapter 2 Empirical Exercises
6.2
Chapter 3 Empirical Exercises
6.3
Chapter 4 Empirical Exercises
7
Method Exercises
7.1
Chapter 2 Method Exercises
7.1.1
Section 2.2 Method Exercises
7.1.2
Section 2.3 Method Exercises
7.1.3
Section 2.4 Method Exercises
7.2
Chapter 3 Method Exercises
7.2.1
Section 3.2 Method Exercises
7.2.2
Section 3.3 Method Exercises
7.3
Chapter 4 Method Exercises
7.3.1
Section 4.1 Method Exercises
7.4
Chapter 5 Method Exercises
7.5
Chapter 6 Method Exercises
8
Appendix: Data Dictionary
8.1
United States Population Mortality Counts
8.2
Synthetic Insurer Data
8.3
Canine Mortality
8.4
Canadian Female Select and Ultimate Mortality Table
8.5
Korean Mortality by Insured Status
Korean Mortality - Insured Lives
Korean Mortality - Annuitants
Korean Mortality - Population
8.6
Mortality by Country
Population Mortality - Japan
Population Mortality - Poland
Population Mortality - United States
8.7
Disability Income
Disability Recovery Rates - Male
Disability Recovery Rates - FeMale
Death and Disability Recovery Rates - Male
Death and Disability Recovery Rates - Female
9
Appendix: Conventions for Notation
9.1
Actuarial Notation
9.1.1
Life Table Symbols
9.1.2
Life Insurance Symbols
9.1.3
Annuity Certain and Life Annuity Symbols
9.2
Halo System
9.3
General Conventions
9.4
Abbreviations
9.5
Common Statistical Symbols and Operators
9.6
Common Mathematical Symbols and Functions
9.7
Further Readings
Bibliography
Life Contingencies on GitHub
Life Contingencies: The Mathematics, Statistics, and Economics of Life Insurance
Chapter 1
Introduction
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