Prediction of Outstanding Insurance Claims

Building reserves for outstanding liabilities is an important issue in the nancial statement of any insurance company. In this paper we present a new model for delay in claim settlement and to predict IBNR (incurred but not reported) claims. The modelling is based on a data set of a portfolio of car liability data, which describes the claim settlement of a car insurance portfolio. The data consists of about 5 000 realisations of claims, all of which incurred in 1985 and were followed until the end of 1993. In our model, the total claim amount process (S(t)) t0 is described by a Poisson shot noise model, i.e