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An Extension of Mack's Model for the Chain Ladder Method

Published online by Cambridge University Press:  29 August 2014

Klaus D. Schmidt  and
Anja Schnaus
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Abstract

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The chain ladder method is a simple and suggestive tool in claims reserving, and various attempts have been made aiming at its justification in a stochastic model. Remarkable progress has been achieved by Schnieper and Mack who considered models involving assumptions on conditional distributions. The present paper extends the model of Mack and proposes a basic model in a decision theoretic setting. The model allows to characterize optimality of the chain ladder factors as predictors of non-observable development factors and hence optimality of the chain ladder predictors of aggregate claims at the end of the first non-observable calendar year. We also present a model in which the chain ladder predictor of ultimate aggregate claims turns out to be unbiased.

Type
Workshops
Information
ASTIN Bulletin: The Journal of the IAA , Volume 26 , Issue 2 , November 1996 , pp. 247 - 262
Copyright
Copyright © International Actuarial Association 1996

References

Mack, T. (1993) Distribution-free calculation of the standard error of chain ladder reserve estimates. ASTIN Bull. 23, 213–225.CrossRefGoogle Scholar
Mack, T. (1994a) Which stochastic model is underlying the chain ladder method? Insurance Math. Econom. 15, 133–138.CrossRefGoogle Scholar
Mack, T. (1994b) Measuring the variability of chain ladder reserve estimates. Casualty Actuarial Society Forum Spring 1994, vol. 1, 101–182.Google Scholar
Schnieper, R. (1991) Separating true IBNR and IBNER claims. ASTIN Bull. 21, 111–127.CrossRefGoogle Scholar