Analyzing Casualty Insurance Claim Counts

Abstract

When a property or casualty insurer accepts a payment of premium in return for exposure to loss, the insurer must establish a liability account, called a loss reserve, which estimates the amount of the expected loss. Accurate estimation of the expected loss is important both for the preparation of realistic financial statements and for the establishment of profitable premium rates. However, the initial loss reserve is only the beginning of the estimation problem. As the time since the period of exposure increases, the probability of a claim and hence the expectation of loss diminishes. At the same time, if a claim is made, the particular details of the claim can be used to produce a more precise estimate of loss called a case reserve. As the claim is processed, the case reserve is adjusted for payments made and new information obtained. Eventually, both types of loss reserves are eliminated and the ultimate realized loss is the total of all known payments. The estimates of claims rates and loss severities must be based on prior loss information. Because of reporting and processing delays, the most recent and hence most relevant of this information will be incomplete. Thus, the real challenge in the analysis of casualty insurance loss information is to develop methods of obtaining estimates of ultimate loss that are conditional on the current structurally incomplete loss data base.