The Reserve uncertainties in the chain ladder model of mack revisited

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<title>Reserve uncertainties in the chain ladder model of mack revisited</title>
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<abstract displayLabel="Summary">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 MerzWüthrich. Our uncertainty estimators of the one-year run-off risks are new and different to the MerzWüthrich 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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<note type="statement of responsibility">Alois Gisler</note>
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<topic>Teorema de Bayes</topic>
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<topic>Predicciones estadísticas</topic>
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<topic>Cálculo actuarial</topic>
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<title>Astin bulletin</title>
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<publisher>Belgium : ASTIN and AFIR Sections of the International Actuarial Association</publisher>
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<identifier type="issn">0515-0361</identifier>
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<text>02/09/2019 Volumen 49 Número 3 - septiembre 2019 , p. 787-821</text>
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