Orient BlackSwan

About the BookAbout the AuthorTable of Contents

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.

Shailaja Deshmukh is a professor of statistics at the University of Pune, India. Her areas of interest are inference in stochastic processes, applied probability and analysis of microarray data. She has authored two books, Microarray Data: Statistical Analysis Using R, (jointly with Dr Sudha Purohit), and Statistics Using R (jointly with Dr Sudha Purohit and Prof Sharad Gore). She has a number of research publications in various peer-reviewed journals.

Preface

Insurance Business

Introduction
What is an Actuarial Science?
Insurance Companies as Business Organisations
Concept of Risk
How Does the Insurance Business Operate?
Role of Statistics in Insurance
Insurance Business in India

Introductory Statistics
Introduction
Some Important Discrete Distributions
Some Important Continuous Distributions
Multivariate Distributions

Feasibility of Insurance Business and Risk Models for Short Term
Introduction
Expected Value Principle
Notion of Utility
Risk Models for Short Term

Future Lifetime Distribution and Life Tables
Introduction
Future Life Time Random Variable
Curate Future - Lifetime
Life Tables
Assumptions for Fractional Ages
Select and Ultimate Life Tables
Computations Using R

Actuarial Present Values of Benefit in Life Insurance Products
Introduction
Compound Interest and Discount Factor
Benefit Payable at the Moment of Death
Benefit Payable at the End of Year of Death
Relation Between A and ¯ A
Computation Using R

Annuities
Introduction
Annuities Certain
Continuous Life Annuities
Discrete Life Annuities
Life Annuities with mthly Payments
Computation Using R

Premiums
Introduction
Loss at Issue Random Variable
Fully Continuous Premiums
Fully Discrete Premiums
True mthly Payment Premiums
Gross Premiums
Computations Using R

Reserves
Introduction
Fully Continuous Reserves
Fully Discrete Reserves
Computation Using R

Multiple Life Contracts
Introduction
Joint Life Status
Last Survivor Status
Computations Using R

Answers to Exercises
References
Index