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Prediction Error of the Chain Ladder Reserving Method applied to Correlated Run-off Triangles

Published online by Cambridge University Press:  10 May 2011

M. Merz  and
M. V. Wüthrich
M. Merz
Affiliation:
University of Tübingen, Faculty of Economics, D-72074, Germany
M. V. Wüthrich
Affiliation:
ETH Zürich, Department of Mathematics, CH-8092 Zürich, Switzerland
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Abstract

In Buchwalder et al. (2006) we revisited Mack's (1993) and Murphy's (1994) estimates for the mean square error of prediction (MSEP) of the chain ladder claims reserving method. This was done using a time series model for the chain ladder method. In this paper we extend the time series model to determine an estimate for the MSEP of a portfolio of N correlated run-off triangles. This estimate differs in the special case N = 2 from the estimate given by Braun (2004). We discuss the differences between the estimates.

Keywords

Claims ReservingChain LadderMean Square Error of PredictionPrediction ErrorCorrelated Business LinesRun Off
Type
Papers
Information
Annals of Actuarial Science , Volume 2 , Issue 1 , March 2007 , pp. 25 - 50
Copyright
Copyright © Institute and Faculty of Actuaries 2007

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References

Ajne, B. (1994). Additivity of chain-ladder projections. Astin Bulletin, 24(2), 313–318.CrossRefGoogle Scholar
Braun, C. (2004). The prediction error of the chain ladder method applied to correlated runoff triangles. Astin Bulletin, 34(2), 399–423.CrossRefGoogle Scholar
Buchwalder, M., Buhlmann, H., Merz, M. & Wuthrich, M.V. (2006). The mean square error of prediction in the chain ladder reserving method (Mack and Murphy revisited). Astin Bulletin, 36(2), 521–542.CrossRefGoogle Scholar
England, P.D. & Verrall, R.J. (1999). Analytic and bootstrap estimates of prediction errors in claims reserving. Insurance: Mathematics and Economics, 25, 281–293.Google Scholar
England, P.D. & Verrall, R.J. (2002). Stochastic claims reserving in general insurance. British Actuarial Journal, 8, 443–518.CrossRefGoogle Scholar
Gisler, A. (2006). The estimation error in the chain-ladder reserving method: a Bayesian approach. Astin Bulletin, 36(2), 554–565.CrossRefGoogle Scholar
Mack, T. (1993). Distribution-free calculation of the standard error of chain ladder reserve estimates. Astin Bulletin, 23, 213–225.CrossRefGoogle 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(2), 543–552.CrossRefGoogle Scholar
Murphy, D.M. (1994). Unbiased loss development factors. Proceedings of the Casualty Actuarial Society, LXXXI, 154–222.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
Venter, G.G. (2006). Discussion of mean square error of prediction in the chain ladder reserving method. Astin Bulletin, 36(2), 566–572.CrossRefGoogle Scholar
Verrall, R.J. (2000). An investigation into stochastic claims reserving models and the chain-ladder technique. Insurance: Mathematics and Economics, 26, 91–99.Google Scholar
Wüthrich, M.V., Merz, M. & Bühlmann, H. (2006). Bounds on the estimation error in the chain ladder method. To appear in Scandinavian Actuarial Journal.Google Scholar