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Experience rating with Poisson mixtures

Published online by Cambridge University Press:  16 July 2015

Garfield O. Brown
Affiliation:
Statistical Laboratory, Centre for Mathematical Sciences, Cambridge, CB3 0WB, UK
Winston S. Buckley*
Affiliation:
Mathematical Sciences, Bentley University, Waltham, MA 02452, USA
*
*Correspondence to: Winston S. Buckley, Mathematical Sciences, Bentley University, Waltham, MA 02452, USA. Tel: 781-891-2000; Fax: 781-891-2457; E-mail: winb365@hotmail.com

Abstract

We propose a Poisson mixture model for count data to determine the number of groups in a Group Life insurance portfolio consisting of claim numbers or deaths. We take a non-parametric Bayesian approach to modelling this mixture distribution using a Dirichlet process prior and use reversible jump Markov chain Monte Carlo to estimate the number of components in the mixture. Unlike Haastrup, we show that the assumption of identical heterogeneity for all groups may not hold as 88% of the posterior probability is assigned to models with two or three components, and 11% to models with four or five components, whereas models with one component are never visited. Our major contribution is showing how to account for both model uncertainty and parameter estimation within a single framework.

Type
Papers
Copyright
© Institute and Faculty of Actuaries 2015 

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