Actuarial Notes

Outstanding Claims Reserves

By Mary R. Hardy · Society of Actuaries · 2022

Study guide: Exam GI-301

A study note, Version 1.3a, written by Mary R. Hardy for the Education Committee of the Society of Actuaries and formatted for SOA Course GI 301, Further Topics in General Insurance. Its author's objective is to present both deterministic and some stochastic methods and models for estimating outstanding claims liabilities, in a form suitable for both classroom teaching and self-study, balancing rigour and accessibility. It uses the R package ChainLadder extensively in Chapters 4 and 5.

On the syllabus

  • Exam GI-301 — Outcomes 1a-d; Ch. 3-5, excluding sections 3.4 and 4.3.

Preface

1 Introduction

  • OCR Categories

2 Run-off triangles

  • 2.1 Notation
  • 2.2 The deterministic chain ladder approach
  • 2.3 Inflation-adjusted chain ladder

3 \hat{C}_{i,J} as an expected value

  • 3.1 The chain ladder method
  • 3.2 Testing the chain ladder assumptions
  • 3.3 The Bornhuetter-Ferguson (BF) method
  • 3.4 The Bühlmann-Straub credibility model
  • 3.5 The Poisson model

4 Mack's model

  • 4.1 Introduction and assumptions
  • 4.2 Uncertainty measures in Mack's model
    • 4.2.1 Process variance
    • 4.2.2 Estimation error, individual AY
    • 4.2.3 MSEP for aggregate outstanding claims
  • 4.3 Mack's Model in R

5 The overdispersed Poisson model

6 Frequency-severity models

  • 6.1 Claim frequency
  • 6.2 Claim severity

Bibliography

Appendix A Proof of Theorem 3

Sources