Statistical and Probabilistic Methods in Actuarial Science: 1st Edition (Hardback) book cover

Statistical and Probabilistic Methods in Actuarial Science

1st Edition

By Philip J. Boland

Chapman and Hall/CRC

368 pages | 25 B/W Illus.

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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.


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

Table of Contents



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

About the Series

Chapman & Hall/CRC Interdisciplinary Statistics

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Subject Categories

BISAC Subject Codes/Headings:
MATHEMATICS / Probability & Statistics / General