Credibility for Treaty Reinsurance Excess Pricing

Treaty reinsurance excess pricing ideally consists of both an exposure rating and an experience rating. The problem is how to put them together to reach a final rate. This paper uses Hans Buhlmann’s 1967 least squares credibility formulation for computing the final rate. We extend Erwin Straub’s 1971 excess credibility model by considering uncertainty in the excess claims probability in addition to the uncertainty in the group-up claim count expectation. We tie together excess credibility for various attachment points into a consistent model utilizing a gamma/Poisson model for the ground-up number of claims. We discuss the a priori information available for excess exposure rating in the US casualty market and its problems. Likewise, we discuss the problems inherent in the normal reinsurance excess experience rating methodology. We discuss the question of subjectivity with regard to the information available in various actual pricing situations, and present a questionnaire designed to elicit and codify an underwriter’s judgment leading to an appropriate credibility structure. This paper is written for reinsurance practitioners. Reinsurance Research - Pricing/Contract Design