Estimation of the Number of Excess Claims by Means of the Credibility Theory

The purpose of this paper is to describe a possible application on the rating of excess of loss covers of Mr. Buhlmann's work on Experience Rating and Credibility. One of the most important problems in connection with the rating of such treaties consists in estimating the number of excess claims and the average excess claim amount. Especially with cases where claims data are scarce there is a temptation to estimate these two quantities by means of the credibility theory. This approach leads, on the one hand, to a relatively complicated formula when considering the average excess claim amount, and, on the other, to a rather simple one for the credibility factor of the number of excess claims.