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Bayes and Empirical Bayes Estimation for the Chain Ladder Model

Published online by Cambridge University Press:  29 August 2014

R.J. Verrall
R.J. Verrall*
Affiliation:
City University, London, United Kingdom
*
Department of Actuarial Science and Statistics, City University, Northampton Square London EC1V OHB
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Abstract

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The subject of predicting outstanding claims on a porfolio of general insurance policies is approached via the theory of hierarchical Bayesian linear models. This is particularly appropriate since the chain ladder technique can be expressed in the form of a linear model. The statistical methods which are applied allow the practitioner to use different modelling assumptions from those implied by a classical formulation, and to arrive at forecasts which have a greater degree of inherent stability. The results can also be used for other linear models. By using a statistical structure, a sound approach to the chain ladder technique can be derived. The Bayesian results allow the input of collateral information in a formal manner. Empirical Bayes results are derived which can be interpreted as credibility estimates. The statistical assumptions which are made in the modelling procedure are clearly set out and can be tested by the practitioner. The results based on the statistical theory form one part of the reserving procedure, and should be followed by expert interpretation and analysis. An illustration of the use of Bayesian and empirical Bayes estimation methods is given.

Type
Workshop
Information
ASTIN Bulletin: The Journal of the IAA , Volume 20 , Issue 2 , November 1990 , pp. 217 - 243
Copyright
Copyright © International Actuarial Association 1990

References

Buhlmann, H. (1967) Experience Rating and credibility. ASTIN Bulletin, Vol. 4, No. 3, 199–207.CrossRefGoogle Scholar
Goovaerts, and Hoogstad, (1987) Credibility Theory. Surveys of Actuarial Studies, No. 4.Google Scholar
Klugman, S. (1989) Credibility for Classification Ratemaking via the Hierarchical Normal Linear Model. Proc. of Casualty Actuarial Society, Vol. 74, 272–321.Google Scholar
Kremer, E. (1982) IBNR-Claims and the Two-Way Model of ANOVA. Scand. Act. J., Vol. 1, 47–55.CrossRefGoogle Scholar
Lindley, D.V. and Smith, A.P.M. (1972) Bayes Estimates for the Linear Model (with Discussion) JRSS, Series B, Vol. 34, No. 1, 1–41.Google Scholar
Smith, A. F. M. (1973) A General Bayesian Linear Model. JRSS, Series B, Vol. 35, No. 1, 67–75.Google Scholar
Taylor, G.C. and Ashe, F. R. (1983) Second Moments of Estimates of Outstanding Claims. J. of Econometrics, Vol. 23, 37–61.CrossRefGoogle Scholar
Verrall, R.J. (1988) Bayesian Linear Models and the Claims Run-off Triangle. Actuarial Research Paper, No. 7, The City University, London.Google Scholar
Verrall, R.J. (1989a) On the Unbiased Estimation of Reserves from Loglinear Models. Insurance: Mathematics and Economics, to appear.Google Scholar
Verrall, R.J. (1989b) Chain Ladder and Maximum Likelihood. Under review.Google Scholar
Verrall, R.J. (1989c) A State Space Representation of the Chain Ladder Linear Model. Applications of Mathematics in Insurance, Finance and Accounting Work; joint meeting of the Institute and Faculty of Actuaries and the Institute of Mathematics and its Applications. Journal of the Institute of Actuaries, Vol. 116, Part. III, 589–610.CrossRefGoogle Scholar
De Vylder, F. (1982) Estimation of IBNR claims by Credibility Theory. Insurance: Mathematics and Economics, 1, 35–40.Google Scholar