WIAS Preprint No. 1519, (2010)

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



Authors

  • Krätschmer, Volker
  • Zähle, Henryk

2010 Mathematics Subject Classification

  • 60F05 62F12 91B30

Keywords

  • 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

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.

Appeared in

  • Insurance Math. Econom., 49 (2011) pp. 335--344.

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