Credibility for a Tower of Excess Layers

In pricing excess of loss reinsurance, the traditional method for applying credibility is as a weighted average of two estimates of expected loss: one from experience rating and a second from exposure rating. This paper will show how this method can be improved by incorporating loss estimates from lower layers, thus producing a multi-factor, credibility-weighted estimate of expected loss.

The method described is based on minimum variance criteria, whereby the resulting credibility-weighted estimator has a lower variance than any other combination of the individual estimators. It is shown that the multi-factor credibility model can be presented as a simple recursive procedure for practical application.

Keywords: Excess of loss reinsurance, exposure rating, credibility