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Quasi-Hadamard differentiability of general risk functionals and its application

Author

Listed:
  • Krätschmer Volker

    (Faculty of Mathematics, University of Duisburg–Essen, Germany)

  • Schied Alexander

    (Department of Mathematics, University of Mannheim, Germany)

  • Zähle Henryk

    (Department of Mathematics, Saarland University, Germany)

Abstract

We apply a suitable modification of the functional delta method to statistical functionals that arise from law-invariant coherent risk measures. To this end we establish differentiability of the statistical functional in a relaxed Hadamard sense, namely with respect to a suitably chosen norm and in the directions of a specifically chosen “tangent space”. We show that this notion of quasi-Hadamard differentiability yields both strong laws and limit theorems for the asymptotic distribution of the plug-in estimators. Our results can be regarded as a contribution to the statistics and numerics of risk measurement and as a case study for possible refinements of the functional delta method through fine-tuning the underlying notion of differentiability.

Suggested Citation

  • Krätschmer Volker & Schied Alexander & Zähle Henryk, 2015. "Quasi-Hadamard differentiability of general risk functionals and its application," Statistics & Risk Modeling, De Gruyter, vol. 32(1), pages 25-47, April.
    • Handle: RePEc:bpj:strimo:v:32:y:2015:i:1:p:25-47:n:4
    DOI: 10.1515/strm-2014-1174
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    References listed on IDEAS

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