Abstract

Journal of Actuarial Practice

Volume 13, 2006

Bayesian Analysis of Insurance Losses Using the Bühlmann-Straub Credibility Model

Abraham J. van der Merwe and Kobus N. Bekker

Abstract

We propose a Bayesian analysis to develop credibility estimates of the well-known Bühlmann-Straub model. We describe simple numerical methods to obtain exact posterior distributions and predictive densities under this model. These distributions are obtained through Monte Carlo simulations that generate independent samples from the joint posterior distribution. Our methods are therefore preferable to methods such as Gibbs sampling, which generates dependent samples from the joint distribution. The methods discussed also can be extended to more complicated credibility models.

Key words and phrases: Bayesian procedure, credibility theory, Monte Carlo simulation, probability-matching prior, reference priors

Corresponding Author:

Kobus N. Bekker

Department of Mathematical Statistics,

University of the Free State

PO Box 339

Bloemfontein 9300,

SOUTH AFRICA

E-mail: bekkerkn.sci@mail.uovs.ac.za