Statistical and Probabilistic Methods in Actuarial Science

Covering many of the diverse methods in applied probability and statistics, this book builds on readers' 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. The applications to general insurance include loss distributions and collective risk models, reserving and experience rating, credibility estimation, and security measures of risk. The book examines generalized linear models, credibility theory, game theory, and simulation techniques and contains numerous worked examples and problems.

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.

PREFACE 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