Stochastic Claims Reserving When Past Claim Numbers Are Known

This paper addresses the problem of estimating future claim payments when two run-off triangles are available: one of the number of claims, the other of total amounts. Each single claim can have partial payments included in the total for several development periods. The method does not require additional information, such as measures of exposure and claims inflation. The approach adopted is to model the mean claim amount as a function of operational time, using generalized linear models. Techniques are described for fitting and comparing a number of models of this type, and for predicting the total of future claims from the best fitting model. Formal statistical tests are used for comparing models. It is shown how the root-mean-square (RMS) error of prediction can be calculated, making due allowance for modelling error and random variation in both the number and amounts of future payments. Models are formulated to make explicit allowance for claims inflation and partial payments. Assumptions are minimal, and diagnostic techniques are described for checking their validity in each application. Numerical examples are given.