Uncertainty-based Credibility and its Application to Excess-of-loss Reinsurance

This paper proposes a methodology to calculate the credibility risk premium based on the uncertainty on the risk premium, as estimated by the standard deviation of the risk premium estimator. An optimal estimator based on the uncertainties involved in the pricing process is constructed.

The methodology is then applied to pricing layers of excess-of-loss reinsurance, and the behaviour of the credibility factor as a function of layer excess is analysed. Results are obtained for both the general case and the significant special case where the severity distribution is the same for all clients, for which it is proved that credibility is broadly constant across the reinsurance layers. A real-world application to pricing motor reinsurance is also discussed.

Although the methodology is especially useful when applied to reinsurance, the underlying ideas are completely general and can be applied to all contexts where the uncertainties in the pricing process can be calculated.

Keywords: uncertainty-based credibility, pricing horizon, excess-of-loss reinsurance pricing, market heterogeneity, error propagation analysis