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Mean Square Error of Prediction in the Bornhuetter–Ferguson Claims Reserving Method

Published online by Cambridge University Press:  10 May 2011

D. H. Alai ,
M. Merz  and
M. V. Wüthrich
M. V. Wüthrich
Affiliation:
ETH Zurich, Department of Mathematics, 8092 Zurich, Switzerland., Email: [email protected]
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Abstract

The prediction of adequate claims reserves is a major subject in actuarial practice and science. Due to their simplicity, the chain ladder (CL) and Bornhuetter–Ferguson (BF) methods are the most commonly used claims reserving methods in practice. However, in contrast to the CL method, no estimator for the conditional mean square error of prediction (MSEP) of the ultimate claim has been derived in the BF method until now, and as such, this paper aims to fill that gap. This will be done in the framework of generalized linear models (GLM) using the (overdispersed) Poisson model motivation for the use of CL factor estimates in the estimation of the claims development pattern.

Keywords

Claims ReservingBornhuetter–FergusonOverdispersed Poisson DistributionChain Ladder MethodGeneralized Linear ModelsConditional Mean Square Error of Prediction
Type
Papers
Information
Annals of Actuarial Science , Volume 4 , Issue 1 , March 2009 , pp. 7 - 31
Copyright
Copyright © Institute and Faculty of Actuaries 2009

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References

Bornhuetter, R.L. & Ferguson, R.E. (1972). The actuary and IBNR. Proceedings of the Casualty Actuarial Society, LIX, 181–195.Google Scholar
Bühlmann, H. & Gisler, A. (2005). A course in credibility theory and its applications. Springer, Berlin.Google Scholar
Casualty Actuarial Society (1990). Foundations of casualty actuarial science. 4th ed.Casualty Actuarial Society, New York.Google Scholar
England, P.D. & Verrall, R.J. (2002). Stochastic claims reserving in general insurance. British Actuarial Journal, 8, 443–518.CrossRefGoogle Scholar
England, P.D. & Verrall, R.J. (2007). Predictive distributions of outstanding liabilities in general insurance. Annals of Actuarial Science, 1, 221–270.CrossRefGoogle Scholar
Fahrmeir, L. & Tutz, G. (2001). Multivariate statistical modelling based on generalized linear models. 2nd ed.Springer, Berlin.CrossRefGoogle Scholar
Hachemeister, C. & Stanard, J. (1975). IBNR claims count estimation with static lag functions. Presented at ASTIN Colloquium, Portimao, Portugal.Google Scholar
Lambrigger, D.D., Shevchenko, P.V. & Wuthrich, M.V. (2007). The quantification of operational risk using internal data, relevant external data and expert opinion. Journal of Operational Risk, 2, 3–27.CrossRefGoogle Scholar
Mack, T. (1991). A simple parametric model for rating automobile insurance or estimating IBNR claims reserves. ASTIN Bulletin, 21, 93–109.CrossRefGoogle Scholar
Mack, T. (1993). Distribution-free calculation of the standard error chain ladder reserves estimates. ASTIN Bulletin, 23, 213–225.CrossRefGoogle Scholar
Mack, T. (2000). Credible claims reserves: The Benktander method. ASTIN Bulletin, 30, 333–347.CrossRefGoogle Scholar
Mack, T. (2006). Parameter estimation for Bornhuetter/Ferguson. CAS Forum, Fall 2006, 141–157.Google Scholar
Mack, T., Quarg, G. & Braun, C. (2006). The mean square error of prediction in the chain ladder reserving method — a comment. ASTIN Bulletin, 36, 543–552.CrossRefGoogle Scholar
McCullagh, P. & Nelder, J.A. (1989). Generalized linear models. 2nd ed.Chapman and Hall, London.CrossRefGoogle Scholar
Panjer, H.H. (2006). Operational risk: modeling analytics. Wiley, New York.CrossRefGoogle Scholar
Radtke, M. & Schmidt, K.D. (2004). Handbuch zur Schadenreservierung. Verlag Versicherungswirtschaft, Karlsruhe.Google Scholar
Renshaw, A.E. (1995). Claims reserving by joint modelling. Presented at ASTIN Colloquium, Cannes.Google Scholar
Renshaw, A.E. & Verrall, R.J. (1998). A stochastic model underlying the chain ladder technique. British Actuarial Journal, 4, 903–923.CrossRefGoogle Scholar
Swiss Solvency Test (2006). BPV SST Technisches Dokument, Version October 2, 2006.Google Scholar
Taylor, G. (2000). Loss reserving: an actuarial perspective. Kluwer Academic Publishers, Boston.CrossRefGoogle Scholar
Teugels, J.L. & Sundt, B. (2004). Encyclopedia of actuarial science. Volume 1. Wiley, Chichester.CrossRefGoogle Scholar
Verrall, R.J. (1990). Bayesian and empirical Bayes estimation for the chain ladder model. ASTIN Bulletin, 20, 217–238.CrossRefGoogle Scholar
Verrall, R.J. (2000). An investigation into stochastic claims reserving models and the chain-ladder technique. Insurance: Mathematics & Economics, 26, 91–99.Google Scholar
Verrall, R.J. (2004). A Bayesian generalized linear model for the Bornhuetter–Ferguson method of claims reserving. North American Actuarial Journal, 8, 67–89.CrossRefGoogle Scholar
Verrall, R.J. & England, P.D. (2000). Comments on: “A comparison of stochastic models that reproduce chain ladder reserve estimates”, by Mack and Venter. Insurance: Mathematics & Economics, 26, 109–111.Google Scholar
Wüthrich, M.V., Merz, M. & Buhlmann, H. (2008). Bounds on the estimation error in the chain ladder method. Scandinavian Actuarial Journal, 4, 283–300.CrossRefGoogle Scholar