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Title:Sensitivity of risk measures with respect to the normal approximation of total claim distributions PDF Logo
Authors:Krätschmer, Volker
Zähle, Henryk
Issue Date:2010
Series/Report no.:SFB 649 discussion paper 2010,033
Abstract:A simple and commonly used method to approximate the total claim distribution of a (possible weakly dependent) insurance collective is the normal approximation. In this article, we investigate the error made when the normal approximation is plugged in a fairly general distribution-invariant risk measure. We focus on the rate of the convergence of the error relative to the number of clients, we specify the relative error's asymptotic distribution, and we illustrate our results by means of a numerical example. Regarding the risk measure, we take into account distortion risk measures as well as distribution-invariant coherent risk measures.
Subjects:total claim distribution
[phi]- and [alpha]-mixing sequences of random variables
normal approximation
nonuniform Berry-Esseen inequality
distortion risk measure
coherent risk measure
robust representation
JEL:G22
G32
Document Type:Working Paper
Appears in Collections:SFB 649 Discussion Papers, HU Berlin

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