A Bayesian Approach to Excess of Loss Pure Premium Rating

This paper demonstrates a Bayesian approach for estimating loss costs associated with excess of loss reinsurance programs. The main features of this approach are that (1) prior severity dis-tributions are adjusted for historical emergence patterns under-lying the experience data, (2) maximum likelihood estimation is used to estimate a ground-up loss ratio for each prior severity distribution, (3) a posterior severity distribution is derived using a Bayesian approach, and (4) a posterior ground-up loss ratio is derived using a Bayesian approach. This paper illustrates a simple implementation of the approach and tests the model by simulating from known frequency and severity distributions and fitting the model to the simulated “data.”