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THE RESERVE UNCERTAINTIES IN THE CHAIN LADDER MODEL OF MACK REVISITED

  • Alois Gisler (a1)

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.

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Bühlmann, H., De Felice, M., Gisler, A. and Wüthrich, M.V. (2009) Recursive credibility formulas for chain ladder factors and the claims development result. ASTIN Bulletin, 39(1), 275306.
Diers, D., Linde, M. and Hahn, L. (2016) Quantification of multi-year non-life insurance risk in chain ladder reserving models. Insurance: Mathematics and Economics, 67, 187199.
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Wüthrich, M.V., Merz, M. and Lysenko, N. (2009). Uncertainty of the claims development result in the chain ladder method. Scandinavian Actuarial Journal, 2009(1), 6384.

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