19 - Claims Triangles

Summary

Chapter Preview. This chapter introduces a classic actuarial reserving problem that is encountered extensively in property and casualty as well as health insurance. The data are presented in a triangular format to emphasize their longitudinal and censored nature. This chapter explains how such data arise naturally and introduces regression methods to address the actuarial reserving problem.

Introduction

In many types of insurance, little time elapses between the event of a claim, notification to an insurance company, and payment to beneficiaries. For example, in life insurance notification and benefit payments typically occurs within two weeks of an insured's death. However, for other lines of insurance, times from claim occurrence to the final payment can be much longer, taking months and even years. To introduce this situation, this section describes the evolution of a claim; introduces summary measures used by insurers, and then describes the prevailing deterministic method for forecasting claims, the chain-ladder method.

Claims Evolution

For example, suppose that you become injured in an automobile accident covered by insurance. It can take months for the injury to heal and all of the medical care payments to become known and paid by the insurance company. Moreover, disputes may arise among you, other parties to the accident, your insurer, and insurer(s) of other parties, thus lengthening the time until claims are settled and paid. When claims take a long time to develop, an insurer's claim obligations may be incurred in one accounting period, but not paid until a later accounting period.