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Stochastic Claims Reserving in General Insurance

Published online by Cambridge University Press:  10 June 2011

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

This paper considers a wide range of stochastic reserving models for use in general insurance, beginning with stochastic models which reproduce the traditional chain-ladder reserve estimates. The models are extended to consider parametric curves and smoothing models for the shape of the development run-off, which allow extrapolation for the estimation of tail factors. The Bornhuetter-Ferguson technique is also considered, within a Bayesian framework, which allows expert opinion to be used to provide prior estimates of ultimate claims. The primary advantage of stochastic reserving models is the availability of measures of precision of reserve estimates, and in this respect, attention is focused on the root mean squared error of prediction (prediction error). Of greater interest is a full predictive distribution of possible reserve outcomes, and different methods of obtaining that distribution are described. The techniques are illustrated with examples throughout, and the wider issues discussed, in particular, the concept of a ‘best estimate’; reporting the variability of claims reserves; and use in dynamic financial analysis models.

Keywords

Stochastic ReservingGeneral InsuranceChain-LadderBornhuetter-FergusonGeneralised Linear ModelGeneralised Additive ModelBayesianBootstrapSimulationMarkov Chain Monte CarloDynamic Financial Analysis
Type
Sessional meetings: papers and abstracts of discussions
Information
British Actuarial Journal , Volume 8 , Issue 3 , 01 August 2002 , pp. 443 - 518
Copyright
Copyright © Institute and Faculty of Actuaries 2002

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