1st Edition
Statistical and Probabilistic Methods in Actuarial Science
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.
INTRODUCTION
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
Problems
Loss Distributions
Introduction to Loss Distributions
Classical Loss Distributions
Fitting Loss Distributions
Mixture Distributions
Loss Distributions and Reinsurance
Problems
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
Problems
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
Problems
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
Problems
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
Problems
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
Problems
Decision and Game Theory
Introduction
Game Theory
Decision making and Risk
Utility and Expected Monetary Gain
Problems
References
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
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, 2007This 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 2008This is a very nice book.
—Tonglin Zhang, Mathematical Reviews, 2009a
