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A Stochastic Model Underlying the Chain-Ladder Technique

Published online by Cambridge University Press:  10 June 2011

A.E. Renshaw  and
R.J. Verrall
R.J. Verrall
Affiliation:
Department of Actuarial Science & Statistics, The City University, Northampton Square, London, EC1V 0HB, U.K. Tel: +44(0)171-477-8476; Fax: +44(0)171-477-8838; E-mail: [email protected]
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Abstract

This paper presents a statistical model underlying the chain-ladder technique. This is related to other statistical approaches to the chain-ladder technique which have been presented previously. The statistical model is cast in the form of a generalised linear model, and a quasi-likelihood approach is used. It is shown that this enables the method to process negative incremental claims. It is suggested that the chain-ladder technique represents a very narrow view of the possible range of models.

Keywords

Chain-Ladder TechniqueClaims ReservingGeneralised Linear ModelsRun-Off Triangles
Type
Sessional meetings: papers and abstracts of discussions
Information
British Actuarial Journal , Volume 4 , Issue 4 , 01 October 1998 , pp. 903 - 923
Copyright
Copyright © Institute and Faculty of Actuaries 1998

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References

REFERENCES

Firth, D. (1988). Multiplicative errors: log-normal or gamma? J.R.S.S. Series B, 50, 266–268.Google Scholar
Francis, B., Green, M. & Payne, C. (1993). The GLIM system. Release 4 Manual, Clarendon Press, Oxford.CrossRefGoogle Scholar
Kremer, E. (1982). IBNR-claims and the two-way model of ANOVA. Scand. Act. J. 1, 47–55.CrossRefGoogle Scholar
McCullagh, P. & Nelder, J.A. (1989). Generalized linear models. Second edition, New York: Chapman and Hall.CrossRefGoogle Scholar
Mack, T. (1991). A simple parameteric model for rating automobile insurance or estimating IBNR claims reserves. ASTIN Bulletin, 22, 93–109.CrossRefGoogle Scholar
Mack, T. (1994). Which stochastic model is underlying the chain ladder method? Insurance: Mathematics and Economics, 15, 133–138.Google Scholar
Renshaw, A. E. (1989). Chain ladder and interactive modelling (claims reserving and GLIM). J.I.A. 116, 559–587.Google Scholar
Renshaw, A. E. (1993). On the application of exponential dispersion models in premium rating. ASTIN Bulletin, 23, 145–148.CrossRefGoogle Scholar
Renshaw, A. E. (1994a). Modelling the claims process in the presence of covariates. ASTIN Bulletin, 24, 265–285.CrossRefGoogle Scholar
Renshaw, A. E. (1994b). A note on some practical aspects of modelling the claims process in the presence of covariates. Proceedings of the XXV ASTIN Colloquium, Cannes.Google Scholar
Rosenberg, P. S. (1990). A simple correction of AIDS surveillance data for reporting delays. J. AIDS, 3, 49–54.Google ScholarPubMed
Verrall, R. J. (1989). A state space representation of the chain ladder linear model. J.I.A. 116, 589–610.Google Scholar
Verrall, R. J. (1990). Bayes and empirical Bayes estimation for the chain ladder model. ASTIN Bulletin, 20, No. 2, 217–243.CrossRefGoogle Scholar
Verrall, R. J. (1991a). On the unbiased estimation of reserves from loglinear models. Insurance: Mathematics and Economics, 10, No. 1, 75–80.Google Scholar
Verrall, R. J. (1991b). Chain ladder and maximum likelihood. J.I.A. 118, 489–499.Google Scholar