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

Author

Listed:
  • Volker Krätschmer
  • Henryk Zähle

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.

Suggested Citation

  • Volker Krätschmer & Henryk Zähle, 2010. "Sensitivity of risk measures with respect to the normal approximation of total claim distributions," SFB 649 Discussion Papers SFB649DP2010-033, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
    • Handle: RePEc:hum:wpaper:sfb649dp2010-033
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    More about this item

    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;
    All these keywords.

    JEL classification:

    • G22 - Financial Economics - - Financial Institutions and Services - - - Insurance; Insurance Companies; Actuarial Studies
    • G32 - Financial Economics - - Corporate Finance and Governance - - - Financing Policy; Financial Risk and Risk Management; Capital and Ownership Structure; Value of Firms; Goodwill

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