Sensitivity of risk measures with respect to the normal approximation of total claim distributions

Volker Krätschmer and Henryk Zähle

Insurance: Mathematics and Economics, 2011, vol. 49, issue 3, 335-344

Abstract: A simple and commonly used method to approximate the total claim distribution of a (possibly 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 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.

Keywords: Total claim distribution; φ- and α-mixing sequences of random variables; Normal approximation; Nonuniform Berry–Esseen inequality; Distortion risk measure; Coherent risk measure; Robust representation (search for similar items in EconPapers)
Date: 2011
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Citations: View citations in EconPapers (6)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:insuma:v:49:y:2011:i:3:p:335-344

DOI: 10.1016/j.insmatheco.2011.05.004

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