Estimating incurred claims

The problem of estimating the final amount after settlement of Motor and General Third Party claims incurred during an underwriting year is of considerable importance for direct writing companies, as well as for reinsurers. While methods of considerable precision have been proposed for direct writing companies' business (ref. 1,2), a less exact but simpler method, which is applicable, i.a., to non-proportional reinsurance, could also be of interest.The method uses the so-called “chain relatives†(ref. 3) computed from the figures for incurred losses similar to those quoted on p. 157, ref. 1. The year in which losses Si,j have occurred is designated by the subscript i, whilst the years in which the corresponding amount of losses paid plus outstanding has been ascertained (or estimated) are designated by the subscript j.“Chain relatives†are defined as a ratio If the available statistics embrace n years, ai,j can be computed for every j = 1, 2, 3, … n—1 but only for i ≤ n—j. To obtain estimates of ai,j for every i > n—j up to i = n we shall use E(ai,j)for fixed j.The underlying hypothesis concerning ai,j is that every ai,j consists of a systematic part and of a random part. The random parts can always be assumed to have the mean = 0. For fixed j the systematic parts are a function of the index for the value of money and of several parameters defining the process of claims settlement. The index for the value of money obviously being constant for each fixed j, it is assumed that the other parameters are also constant for fixed j. This, of course, presupposes that the average proportion (over the years of occurrence) of settlement of the incurred losses is independent of their initial volume and of the year of occurrence.