1st Edition

Statistical and Probabilistic Methods in Actuarial Science

By Philip J. Boland Copyright 2007
    368 Pages 25 B/W Illustrations
    by Chapman & Hall

    Statistical and Probabilistic Methods in Actuarial Science covers many of the diverse methods in applied probability and statistics for students aspiring to careers in insurance, actuarial science, and finance. The book builds on students’ existing knowledge of probability and statistics by establishing a solid and thorough understanding of these methods. It also emphasizes the wide variety of practical situations in insurance and actuarial science where these techniques may be used.


    Although some chapters are linked, several can be studied independently from the others. The first chapter introduces claims reserving via the deterministic chain ladder technique. The next few chapters survey loss distributions, risk models in a fixed period of time, and surplus processes, followed by an examination of credibility theory in which collateral and sample information are brought together to provide reasonable methods of estimation. In the subsequent chapter, experience rating via no claim discount schemes for motor insurance provides an interesting application of Markov chain methods. The final chapters discuss generalized linear models and decision and game theory.

    Developed by an author with many years of teaching experience, this text presents an accessible, sound foundation in both the theory and applications of actuarial science. It encourages students to use the statistical software package R to check examples and solve problems.

    Claims Reserving and Pricing with Run-Off Triangles
    The Evolving Nature of Claims and Reserves
    Chain Ladder Methods
    The Average Cost per Claim Method
    The Bornhuetter-Ferguson or Loss Ratio Method
    An Example in Pricing Products
    Statistical Modeling and the Separation Technique
    Loss Distributions
    Introduction to Loss Distributions
    Classical Loss Distributions 
    Fitting Loss Distributions
    Mixture Distributions
    Loss Distributions and Reinsurance
    Risk Theory
    Risk Models for Aggregate Claims
    Collective Risk Models
    Individual Risk Models for S
    Premiums and Reserves for Aggregate Claims 
    Reinsurance for Aggregate Claims 
    Ruin Theory
    The Probability of Ruin in a Surplus Process
    Surplus and Aggregate Claims Processes
    Probability of Ruin and the Adjustment Coefficient
    Reinsurance and the Probability of Ruin
    Credibility Theory
    Introduction to Credibility Estimates
    Classical Credibility Theory
    The Bayesian Approach to Credibility Theory
    Greatest Accuracy Credibility Theory
    Empirical Bayes Approach to Credibility Theory
    No Claim Discounting in Motor Insurance
    Introduction to No Claim Discount Schemes
    Transition in a No Claim Discount System
    Propensity to Make a Claim in NCD Schemes
    Reducing Heterogeneity with NCD Schemes
    Generalized Linear Models
    Introduction to Linear and Generalized Linear Models
    Multiple Linear Regression and the Normal Model
    The Structure of Generalized Linear Models 
    Model Selection and Deviance
    Decision and Game Theory
    Game Theory
    Decision making and Risk
    Utility and Expected Monetary Gain
    Appendix A: Basic Probability Distributions
    Appendix B: Some Basic Tools in Probability and Statistics
    Moment Generating Functions
    Convolutions of Random Variables
    Conditional Probability and Distributions
    Maximum Likelihood Estimation
    Appendix C: An Introduction to Bayesian Statistics
    Bayesian Statistics
    Appendix D: Answers to Selected Problems
    Claims Reserving and Pricing with Run-Off Triangles
    Loss Distributions
    Risk Theory
    Ruin Theory
    Credibility Theory
    No Claim Discounting in Motor Insurance
    Generalized Linear Models
    Decision and Game Theory


    Philip J. Boland

    This book is meant to serve as a textbook for students seeking careers in insurance, actuarial science, or finance. … The author provides a variety of worked examples in each chapter to illustrate the main ideas, with an emphasis on those of more numerical and practical nature. Although good references for further reading are provided, basic knowledge in probability and statistics is required. This book will also serve as a nice reference for an insurance analyst.
    Technometrics, February 2009, Vol. 51, No. 1

    … There are not many other books that cover actuarial topics based on statistical methods in so complete a way as this one. … this book is quite adequate as a companion book for anyone in involved with the mathematical concepts of statistics and probability models in actuarial science, and it is essential in a university library where these topics are taught.
    Journal of Applied Statistics, 2007

    This book is aimed both at students of actuarial science and related subjects and at insurance and actuarial practitioners. … The treatment is clear throughout, with an ample supply of problems and worked examples. The book would be useful both for teachers of actuarial science and for self-study.
    —N.H. Bingham, Imperial College, International Statistical Review, 2007

    … The book has grown out of lecture notes and gives an overview on mathematical techniques used in actuarial practice. The main focus of the book is general insurance (property and casualty insurance, nonlife insurance). Besides theory, the book gives many exercises and presents R code.
    —Mario V. Wüthrich, ETH Zurich, The American Statistician, November 2008

    This is a very nice book.
    —Tonglin Zhang, Mathematical Reviews, 2009a