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  • Alois Gisler (a1)


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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Merz, M. and Wüthrich, M.V. (2014). Claims run-off uncertainty: the full picture. SSRN manuscript 2524352.
Röhr, A. (2016). Chain ladder and error propagation, ASTIN Bulletin, 46(2), 293330.
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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