Actuarial Statistics: An Introduction Using R

Actuarial science is an interdisciplinary science comprising four subjects mathematics, statistics, economics and finance. Statistics plays a key role in laying the foundation of actuarial calculations in the presence of uncertainty in the mortality pattern of society and under varying economical conditions. Actuarial calculations mainly involve determination of premium rates and computation of reserves. This book discusses the application of various basic concepts and statistical techniques in the determination of premiums and reserves for a variety of standard insurance and annuity products, under a variety of conditions. Topics dealt with include application of utility theory to establish the feasibility of the insurance business, short-term risk models, distribution theory related to the future life time random variable, construction of aggregate and select life table, important concepts of financial mathematics, annuities certain, terms, endowment and whole life insurance products, monthly, quarterly, semi-annual and annual life annuities. The numerous algebraic and numerical examples dispersed throughout the book and the variety of problems at the end of each chapter illustrates the concepts effectively. The main feature of the book is the use of R software to compute various monetary functions involved in the insurance business. R commands are given for all the computations and they are also explained, so that a reader, not familiar with R can use it. The command-driven R software brings out very clearly the successive stages in statistical computations.

Contents:

Preface ix 1. Insurance Business 1.1 Introduction 1.2 What is an Actuarial Science? 1.3 Insurance Companies as Business Organisations 1.4 Concept of Risk 1.5 How Does the Insurance Business Operate? 1.6 Role of Statistics in Insurance 1.7 Insurance Business in India 2. Introductory statistics 2.1 Introduction 2.2 Some Important Discrete Distributions 2.3 Some Important Continuous Distributions 2.4 Multivariate Distributions 3. Feasibility of Insurance Business and Risk Models for Short Term 3.1 Introduction 3.2 Expected Value Principle 3.3 Notion of Utility 3.4 Risk Models for Short Term 4. Future Lifetime Distribution and Life Tables 4.1 Introduction 4.2 Future Life Time Random Variable 4.3 Curate Future - Lifetime 4.4 Life Tables 4.5 Assumptions for Fractional Ages 4.6 Select and Ultimate Life Tables 4.7 Computations Using R 5. Actuarial Present Values of Benefit in Life Insurance Products 5.1 Introduction 5.2 Compound Interest and Discount Factor 5.3 Benefit Payable at the Moment of Death 5.4 Benefit Payable at the End of Year of Death 5.5 Relation Between A and ¯ A 5.6 Computation Using R 6. Annuities 6.1 Introduction 6.2 Annuities Certain 6.3 Continuous Life Annuities 6.4 Discrete Life Annuities 6.5 Life Annuities with mthly Payments 6.6 Computation Using R 7. Premiums 7.1 Introduction 7.2 Loss at Issue Random Variable 7.3 Fully Continuous Premiums 7.4 Fully Discrete Premiums 7.5 True mthly Payment Premiums 7.6 Gross Premiums 7.7 Computations Using R 8. Reserves 8.1 Introduction 8.2 Fully Continuous Reserves 8.3 Fully Discrete Reserves 8.4 Computation Using R 9. Multiple Life Contracts 9.1 Introduction 9.2 Joint Life Status 9.3 Last Survivor Status 9.4 Computations Using R Answers to Exercises References Index

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