A Bayesian Approach to Excess of Loss Pure Premium Rating

Abstract

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.”

Volume
13
Issue
1
Page
54-79
Year
2020
Keywords
Bayesian estimation, maximum likelihood estimation, emergence patterns, exposure curves
Categories
Financial and Statistical Methods
Statistical Models and Methods
Bayesian Methods
Publications
Variance
Authors
Jack Barnett

Keep up with the latest CAS news