A Practical Statistical Method of Estimating Claims Liability and Claims Cash Flow

Abstract

A few years ago Scurfield (JSS 18) indicated a method used inone U.K. non-Life Office for estimating claims liability for the Motor class of business. Since that paper was written a considerable amount of development has taken place and it is now used in the office as an effective continuous method, using computer techniques, for estimating claims liability. It has also been used for projecting expected cash flow for claims arising in the past.Whilst it is accepted that the method has limitations, it has been found that an automatic method is required especially in the production of financial models in the non-Life field, and its limitations are outweighed by the fact that there are, in our opinion, no easier methods of producing a satisfactory working model.In the following paper it is the intention to set out briefly the details of the method, then concentrating on the known limitations and the methods so far devised to combat these limitations. In the appendices we have reproduced some computer printout and figures which will provide practical information on the method.The principle behind the method is that the “Run-off” of claims payments for any “year of claim”, or similar cohort of claims, follows a particular pattern which experience has shown to be reasonably stable. We can thus study the pattern of claims payments at each stage of “run-off”, say each month and thus ascertain the average and range of values that the historic pattern shows (Fig. 1).Fig. 1.Period of delay since beginning of claims Period (Years)