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 distributions are adjusted for historical emergence patterns underlying 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.” Address for Correspondence: jbarnet1@gmail.com