Session: 23

General Insurance

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Summary

Claims recovery due to salvage or to the involvement of third party liabilities in the payment of claims, or to partial or total cancellation of reserves for outstanding claims(sucha as a reduction in reserves due to an initial over-estimation of the liability or because of a final tribunal decision favorable to the insurer when there has been legal arbitrage in which the insurer had claimed a larger sum or the claim was denied) can produce negative values in the development triangle used for estimating reserves (IBNR). These negative values complicate the construction and application of statistical models used for this purpose. The traditional 'chain-ladder' method is not affected by negative values. However, it has the disadvantage that is deterministic and hence no probability intervals can be computed for the reserves. More generally, no inference can be made about the estimated reserves. Stochastic models are required to be able to do this. Several procedures are available for the development of this kind of models when negative values are present. Mostly due to Verrall. In this paper we review existing methods and propose a Bayesian alternative. The different methods are compared through their application to real data sets that have previously been analyzed in the literature and to simulated data sets. We propose a simple alternative model, based on Kremer´s original paper.