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Bayesian over-dispersed Poisson model and the Bornhuetter & Ferguson claims reserving method

Published online by Cambridge University Press:  27 February 2012

Peter D. England ,
Richard J. Verrall  and
Mario V. Wüthrich
Peter D. England
Affiliation:
Towers Watson, London, UK
Richard J. Verrall
Affiliation:
Cass Business School, City University, London, UK
Mario V. Wüthrich*
Affiliation:
ETH Zurich, RiskLab, Department of Mathematics, Switzerland
*
*Correspondence to: Mario V. Wüthrich, ETH Zurich, RiskLab, Department of Mathematics, 8092 Zurich, Switzerland. E-mail: mario.wuethrich@math.ethz.ch
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Abstract

We consider the Bayesian over-dispersed Poisson (ODP) model for claims reserving in general insurance. We choose two different types of prior distributions for the parameters and then study the different Bayesian predictors. This study leads, on the one hand, to the classical chain ladder predictor and, on the other hand, to Bornhuetter & Ferguson predictors. We highlight (either analytically or numerically) how these predictors are obtained and how their prediction uncertainty can be determined.

Keywords

Claims reservingOver-dispersed Poisson modelBornhuetter and Ferguson methodChain ladder methodPrediction uncertaintyMean square error of predictionMarkov chain Monte Carlo method
Type
Papers
Information
Annals of Actuarial Science , Volume 6 , Issue 2 , 23 August 2012 , pp. 258 - 283
Copyright
Copyright © Institute and Faculty of Actuaries 2012

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