Estimation error and bootstrapping in the chain-ladder model of Mack

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<title>Estimation error and bootstrapping in the chain-ladder model of Mack</title>
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<abstract displayLabel="Summary">In 2006 there was quite some discussion on how to estimate the conditional estimation error in the chain-ladder (CL) model of Mack. Buchwalder, Bühlmann, Merz and Wüthrich (BBMW) (ASTIN Bull 36(2):521542, 2006) proposed another estimator than the one derived by Mack (ASTIN Bull 23(2):213225, 1993). These two estimators are also found in a broader context by new authors in recent papers. In the present paper we examine the theoretical properties of the two estimators and come to the conclusion that the BBMW estimator has some major deficiencies compared with the Mack estimator. It takes much less information of the observed triangle into account, the averaging is done over inappropriate sets and it does not properly fit to the Mack CL-model.

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<note type="statement of responsibility">Alois Gisler</note>
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<topic>Cálculo actuarial</topic>
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<topic>Modelos actuariales</topic>
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<title>European Actuarial Journal</title>
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<publisher>Cham, Switzerland  : Springer Nature Switzerland AG,  2021-2022</publisher>
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<identifier type="local">MAP20220007085</identifier>
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<text>07/06/2021 Número 1 - junio 2021 , p. 269-283</text>
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