**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