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The Mean Square Error of Prediction in the Chain Ladder Reserving Method (Mack and Murphy Revisited)

Published online by Cambridge University Press:  17 April 2015

Markus Buchwalder ,
Hans Bühlmann ,
Michael Merz  and
Mario V. Wüthrich
Markus Buchwalder
Affiliation:
Bâloise, Aeschengraben 21, CH-4002 Basel, Switzerland
Hans Bühlmann
Affiliation:
ETH Zürich, Department of Mathematics, CH-8092 Zürich, Switzerland
Michael Merz
Affiliation:
University Tübingen, Faculty of Economics, D-72074 Tübingen, Germany
Mario V. Wüthrich
Affiliation:
ETH Zürich, Department of Mathematics, CH-8092 Zürich, Switzerland
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Abstract

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We revisit the famous Mack formula [2], which gives an estimate for the mean square error of prediction MSEP of the chain ladder claims reserving method: We define a time series model for the chain ladder method. In this time series framework we give an approach for the estimation of the conditional MSEP. It turns out that our approach leads to results that differ from the Mack formula. But we also see that our derivation leads to the same formulas for the MSEP estimate as the ones given in Murphy [4]. We discuss the differences and similarities of these derivations.

Type
Articles
Information
ASTIN Bulletin: The Journal of the IAA , Volume 36 , Issue 2 , November 2006 , pp. 521 - 542
Copyright
Copyright © ASTIN Bulletin 2006

References

[1] Buchwalder, M., Bühlmann, H., Merz, M. and Wüthrich, M.V. (2005) Legal valuation portfolio in non-life insurance. Conference paper presented at the 36th International ASTIN Colloquium, 4-7 September 2005, ETH Zürich. available under www.astin2005.ch Google Scholar
[2] Mack, T. (1993) Distribution-free calculation of the standard error of Chain Ladder reserve estimates. Astin Bulletin 23(2), 213–225.CrossRefGoogle Scholar
[3] Mack, T. (1999) The standard error of Chain Ladder reserve estimates: recursive calculation and inclusion of a tail factor. Astin Bulletin 29(2), 361–366.CrossRefGoogle Scholar
[4] Murphy, D.M. (1994) Unbiased loss development factors. Proc. CAS, LXXXI, 154–222.Google Scholar
[5] Schmidt, K.D. and Schnaus, A. (1996). An extension of Mack’s model for the chain ladder method. Astin Bulletin 26(2), 247–262.CrossRefGoogle Scholar