On the Rating of Excess of Loss Reinsurance Treaties with Reinstatement

Abstract

In the present paper a theoretical approach to rate making in excess of loss reinsurance with reinstatement is discussed. This approach is founded on the models and methods of risk theory and in particular on the theory of premium calculation principles. Reinstatement premiums, however, are dependent on the losses occurred and paid by the reinsurer, and are consequently random unlike the usual premiums in direct and reinsurance. Therefore the standard approach of applying premium calculation principles has to be modified appropriately. This is demonstrated here particularly for premium calculation principles based on a utility function and on a loss function approach. In most cases, however, an explicit premium formula cannot be derived. Therefore numerical techniques are applied to obtain premiums in the case that the underlying claim size and claim number distributions are known.