Actuarial Notes

Distributions for Actuaries

By David Bahnemann · Casualty Actuarial Society · 2015 · CAS Monograph No. 2

Study guide: Exam 8

A brief exposition of the standard probability distributions and their applications by property/casualty actuaries. The focus is on the use of parametric distributions fitted to empirical claim data to solve standard actuarial problems, such as the creation of increased limit factors, the pricing of deductibles, and the evaluation of the effect of aggregate limits. It is the second monograph in the CAS Monograph Series, published in 2015.

On the syllabus

  • Exam 8 — objectives B1–B3; Chapters 5 and 6, including errata; the material in Chapters 1-4 is assumed to be familiar.

Foreword

Preface

1 Introduction

  • 1.1 Probability Spaces
  • 1.2 Random Variables and Probability Distributions
  • 1.3 Mathematical Expectation
  • 1.4 Random Samples
  • 1.5 Fitting Distributions
  • 1.6 Problems

2 Claim Size

3 Claim Counts

  • 3.1 An Elementary Claim Process
  • 3.2 Poisson Claim Processes
  • 3.3 Parameter Uncertainty
  • 3.4 Negative Binomial Distributions
  • 3.5 Claim Contagion
  • 3.6 Portfolio Claims
  • 3.7 Problems

4 Aggregate Claims

  • 4.1 A Discrete Example
  • 4.2 Aggregate Distribution Properties
  • 4.3 Approximation by Matching Moments
  • 4.4 Recursion
  • 4.5 Fourier Approximation
  • 4.6 Discontinuities
  • 4.7 Simulation
  • 4.8 Problems

5 Excess Claims

  • 5.1 Excess Claim Size
  • 5.2 Excess Severity
  • 5.3 Layers of Coverage
  • 5.4 Excess Claim Counts
  • 5.5 Inflation Effects
  • 5.6 Aggregate Layer Claims
  • 5.7 Problems

6 Limits and Deductibles

Appendix

  • A.1 Distribution Approximation
  • A.2 Answers to Selected Problems
  • A.3 References

Sources