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THE RESERVE UNCERTAINTIES IN THE CHAIN LADDER MODEL OF MACK REVISITED

Published online by Cambridge University Press:  01 July 2019

Alois Gisler
Alois Gisler*
Affiliation:
Mathematik, RiskLab ETH Zürich, HG J 58 Rämistrasse 101 CH-8092 ZürichSwitzerland
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Abstract

We revisit the “full picture” of the claims development uncertainty in Mack’s (1993) distribution-free stochastic chain ladder model. We derive the uncertainty estimators in a new and easily understandable way, which is much simpler than the derivation found so far in the literature, and compare them with the well known estimators of Mack and of Merz–Wüthrich.

Our uncertainty estimators of the one-year run-off risks are new and different to the Merz–Wüthrich formulas. But if we approximate our estimators by a first order Taylor expansion, we obtain equivalent but simpler formulas. As regards the ultimate run-off risk, we obtain the same formulas as Mack for single accident years and an equivalent but better interpretable formula for the total over all accident years.

Keywords

claims reservingdistribution free chain-ladder modelBayesian chain-ladder modelconditional mean square error of predictionultimate run-off uncertaintyone-year run-off uncertaintiesMack’s formulaWüthrich–Merz formulascost of capital loadingmarket value margin
Type
Research Article
Information
ASTIN Bulletin: The Journal of the IAA , Volume 49 , Issue 3 , September 2019 , pp. 787 - 821
Copyright
© Astin Bulletin 2019 

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References

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