Bayesian Claim Severity with Mixed Distributions

This paper presents a Bayesian technique for adjusting a mixed exponential severity distribution in response to partially-credible observed claim severities. It presents two applications: pricing excess of loss (XOL) reinsurance layers and computing increased limits factors (ILFs). The paper’s Bayesian model uses a Dirichlet distribution over the mixed exponential’s initial mixture weights. The posterior distribution, produced by conditionalizing on the observed claim severities, is computed using a Markov chain Monte Carlo method.