Actuarial Notes

Outstanding Claims Reserves

By Mary R. Hardy · Society of Actuaries · 2022 · ASTAM-21-26

Study guide: Exam ASTAM

A study note, Version 1.4, written to support students preparing for the Advanced Short-Term Actuarial Mathematics (ASTAM) exam of the Society of Actuaries. Its author's aim is to present both deterministic and some stochastic methods and models for estimating outstanding claims liabilities, in a form suitable for 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 ASTAM — ASTAM-21-26: Outstanding Claims Reserves, Version 1.4, 2022, Hardy, M.R. (excluding Appendix).

Preface

1 Introduction

  • Outstanding Claims Reserves (OCR) represent the provision made by an insurer for losses that have been incurred but not yet settled; the delays come from reporting, claims processing and legal proceedings.
  • Short-tail lines have losses reported promptly, with the longest delays no more than around five years; long-tail lines take well over five years to settle all the claims of one year.
  • The reserve may be subdivided into claims that are reported but not (fully) settled (RBNS) and claims that have been incurred but not yet reported, called IBNR or pure IBNR; most methods in the note estimate the total outstanding claims, with IBNR implicitly included.
  • The Unearned Premium Reserve (UPR) is separate: it is the provision made for future potential claims, the unearned part of premiums paid in advance.
  • OCR categories: case-based estimation, the expected loss ratio method, aggregate run-off triangle methods, credibility methods, frequency-severity methods and parametric models.
  • The note focuses on data-driven aggregate claims estimation approaches that use run-off triangle data to project future payments, starting from the deterministic chain ladder.

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

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

  • The Poisson and overdispersed Poisson (ODP) models, with maximum likelihood estimated parameters, give the same estimated outstanding claims as the chain ladder method; the ODP, formulated as a generalized linear model with a log link, gives an alternative to Mack's formulas for estimating standard errors.

6 Frequency-severity models

  • 6.1 Claim frequency
  • 6.2 Claim severity

A Proof of Theorem 3

Sources