Abstract

Bayesian Extreme Value Analysis with an Application to Credibility Estimation

R.-D. Reiss and M. Thomas

University of Siegen

Exact credibility (Bayesian) and linear credibility estimation of the net premium plays a central role in the actuarial business. For evaluating the risk of excess--of--loss reinsurance treaties, the linear credibility estimation was applied in a restricted Pareto model for which the Hill estimator is the MLE (e.g., Hesselager (1993) and Schnieper (1993)). One is confronted with certain deficiencies of this model (Reiss and Thomas, Statistical Analysis of Extreme Values, Birkh\"auser, 1997). Bayesian parameter estimation in a suitably parametrized full Pareto model was explored in a recent paper by Reiss and Thomas (1998). The present paper deals with the exact credibility estimation of the net premium within models of Poisson--Pareto processes.