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

Klaus D. Schmidt; Anja Schnaus

doi:10.2143/AST.26.2.563223

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.

References

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Crossref Citations

This article has been cited by the following publications. This list is generated based on data provided by Crossref.

Schmidt, Klaus D. 1997. Non-optimal prediction by the chain ladder method. Insurance: Mathematics and Economics, Vol. 21, Issue. 1, p. 17.

Kremer, Erhard 1998. More on Robust Lagfactors. Blätter der DGVFM, Vol. 23, Issue. 4, p. 465.

Schmidt, Klaus D. 1999. Chain Ladder Prediction and Asset Liability Management. Blätter der DGVFM, Vol. 24, Issue. 1, p. 1.

Taylor, Greg 2000. Loss Reserving. Vol. 21, Issue. , p. 195.

Hess, Klaus Th. and Schmidt, Klaus D. 2002. A comparison of models for the chain–ladder method. Insurance: Mathematics and Economics, Vol. 31, Issue. 3, p. 351.

England, P.D. and Verrall, R.J. 2002. Stochastic Claims Reserving in General Insurance. British Actuarial Journal, Vol. 8, Issue. 3, p. 443.

Yan Liu and Yinghui Tang 2005. The problems of the outstanding claims reserve and the IBNR claims reserve - a queuing model method. p. 463.

Buchwalder, Markus Bühlmann, Hans Merz, Michael and Wüthrich, Mario V. 2006. The Mean Square Error of Prediction in the Chain Ladder Reserving Method (Mack and Murphy Revisited). ASTIN Bulletin, Vol. 36, Issue. 2, p. 521.

Schmidt, Klaus D. 2012. Loss prediction based on run-off triangles. AStA Advances in Statistical Analysis, Vol. 96, Issue. 2, p. 265.

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Ling, Ang Siew and Hin, Pooi Ah 2015. Internal modelling under Risk-Based Capital (RBC) framework. Vol. 1691, Issue. , p. 050003.

Tuysuz, Sukriye and Pekel, Pervin 2017. A Comparison of Stochastic Claims Reserving Methods. SSRN Electronic Journal ,

Siegenthaler, Filippo 2021. The ultimate prediction uncertainty in the chain-ladder model of Mack: An unbiased estimator. SSRN Electronic Journal ,

Siegenthaler, Filippo 2023. Unbiased estimator for the ultimate claim prediction error in the chain-ladder model of Mack. Annals of Actuarial Science, Vol. 17, Issue. 1, p. 118.

Article contents

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

Abstract

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