IBNR claims reserving using a compound Poisson INAR(1) model
In non-life insurance, reserving models for incurred but not reported (IBNR) claims are extensively studied for estimating and predicting adequate reserves for the company. We propose a Poisson integer-valued autoregressive (INAR) model of order one for closed claim counts and a compound model based on it in which a mixed gamma distribution for claim severities is assumed. The compound model we study takes into account both the IBNyR (incurred but not yet reported) and IBNeR (incurred but not enough reported) claim counts and their payments. Maximum likelihood techniques are applied for estimating the model parameters. A simulation study is conducted to illustrate the results of the estimations, and to compare the performance of different sizes of the loss development triangle. Predictions based on our proposed model are discussed, and the level of estimation accuracy is examined.