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Predictive Distributions of Outstanding Liabilities in General Insurance

Published online by Cambridge University Press:  10 May 2011

P. D. England  and
R. J. Verrall
P. D. England
Affiliation:
EMB Consultancy, Saddlers Court, 64-74 East Street, Epsom KT17 1HB, U.K., Email: peter.england@emb.co.uk
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Abstract

This paper extends the methods introduced in England & Verrall (2002), and shows how predictive distributions of outstanding liabilities in general insurance can be obtained using bootstrap or Bayesian techniques for clearly defined statistical models. A general procedure for bootstrapping is described, by extending the methods introduced in England & Verrall (1999), England (2002) and Pinheiro et al. (2003). The analogous Bayesian estimation procedure is implemented using Markov-chain Monte Carlo methods, where the models are constructed as Bayesian generalised linear models using the approach described by Dellaportas & Smith (1993). In particular, this paper describes a way of obtaining a predictive distribution from recursive claims reserving models, including the well known model introduced by Mack (1993). Mack's model is useful, since it can be used with data sets which exhibit negative incremental amounts. The techniques are illustrated with examples, and the resulting predictive distributions from both the bootstrap and Bayesian methods are compared.

Keywords

BayesianBootstrapChain LadderDynamic Financial AnalysisGeneralised Linear ModelMarkov Chain Monte CarloReserving RiskStochastic Reserving
Type
Papers
Information
Annals of Actuarial Science , Volume 1 , Issue 2 , September 2006 , pp. 221 - 270
Copyright
Copyright © Institute and Faculty of Actuaries 2006

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