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Nonparametric estimation of risk measures of collective risks

Author

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  • Lauer Alexandra
  • Zähle Henryk

    (Department of Mathematics, Saarland University, Postfach 151150, 66041 Saarbrücken, Germany)

Abstract

We consider two nonparametric estimators for the risk measure of the sum of n i.i.d. individual insurance risks where the number of historical single claims that are used for the statistical estimation is of order n. This framework matches the situation that nonlife insurance companies are faced with within the scope of premium calculation. Indeed, the risk measure of the aggregate risk divided by n can be seen as a suitable premium for each of the individual risks. For both estimators divided by n we derive a sort of Marcinkiewicz–Zygmund strong law as well as a weak limit theorem. The behavior of the estimators for small to moderate n is studied by means of Monte-Carlo simulations.

Suggested Citation

  • Lauer Alexandra & Zähle Henryk, 2016. "Nonparametric estimation of risk measures of collective risks," Statistics & Risk Modeling, De Gruyter, vol. 32(2), pages 89-102, March.
    • Handle: RePEc:bpj:strimo:v:32:y:2016:i:2:p:89-102:n:3
    DOI: 10.1515/strm-2015-0014
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    References listed on IDEAS

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    1. Volker Krätschmer & Alexander Schied & Henryk Zähle, 2014. "Comparative and qualitative robustness for law-invariant risk measures," Finance and Stochastics, Springer, vol. 18(2), pages 271-295, April.
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