A Credibility Index for Posterior Ratemaking with Applications to Large Insurance Portfolios

Abstract

Bayesian credibility models for insurance are mostly mathematical intractable due to their complex structure, and therefore the calculation of credibility premiums must be obtained via simulations from the predictive distribution using Markov Chain Monte Carlo (MCMC) methods. However, such simulations are computationally expensive and even prohibitive for large portfolios. In addition, the computations end up being “black-box” procedures for the actuary, as there is no clear expression to know how the observed experience is used to upgrade premiums. In this paper we address these two challenges. At first we propose a simple, but efficient, simulation setup in which simulations are only drawn from the prior distribution, instead of the posterior one. Secondly, we propose a methodology to estimate a closed-form credibility formula from which approximated Bayesian credibility premiums can be computed for any model, therefore allowing for practical interpretations of how the previous claim experience of a policyholder can be used to derive credibility premiums.

Sebastian Felipe Calcetero Vanegas

PhD Candidate Statistics

Sebastian is a PhD candidate in statistics, working on the developement of predictive models for application in non-life insurance.