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

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  • Krätschmer, Volker
  • Zähle, Henryk
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    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.

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    Bibliographic Info

    Article provided by Elsevier in its journal Insurance: Mathematics and Economics.

    Volume (Year): 49 (2011)
    Issue (Month): 3 ()
    Pages: 335-344

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    Handle: RePEc:eee:insuma:v:49:y:2011:i:3:p:335-344

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    Web page: http://www.elsevier.com/locate/inca/505554

    Related research

    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;

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    Cited by:
    1. Bellini, Fabio & Rosazza Gianin, Emanuela, 2012. "Haezendonck–Goovaerts risk measures and Orlicz quantiles," Insurance: Mathematics and Economics, Elsevier, Elsevier, vol. 51(1), pages 107-114.
    2. Ahn, Jae Youn & Shyamalkumar, Nariankadu D., 2014. "Asymptotic theory for the empirical Haezendonck–Goovaerts risk measure," Insurance: Mathematics and Economics, Elsevier, Elsevier, vol. 55(C), pages 78-90.
    3. Tang, Qihe & Yang, Fan, 2012. "On the Haezendonck–Goovaerts risk measure for extreme risks," Insurance: Mathematics and Economics, Elsevier, Elsevier, vol. 50(1), pages 217-227.
    4. Goovaerts, Marc & Linders, Daniël & Van Weert, Koen & Tank, Fatih, 2012. "On the interplay between distortion, mean value and Haezendonck–Goovaerts risk measures," Insurance: Mathematics and Economics, Elsevier, Elsevier, vol. 51(1), pages 10-18.
    5. Ramon Alemany & Catalina Bolance & Montserrat Guillen, 2014. "Accounting for severity of risk when pricing insurance products," Working Papers, Universitat de Barcelona, UB Riskcenter 2014-05, Universitat de Barcelona, UB Riskcenter.
    6. Alemany, Ramon & Bolancé, Catalina & Guillén, Montserrat, 2013. "A nonparametric approach to calculating value-at-risk," Insurance: Mathematics and Economics, Elsevier, Elsevier, vol. 52(2), pages 255-262.

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