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arXiv · 1401.3167

Quasi-Hadamard differentiability of general risk functionals and its application

Volker Krätschmer·Alexander Schied·Henryk Zähle
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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

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Volker Krätschmer, Alexander Schied, Henryk Zähle. 2014-01-14. Quasi-Hadamard differentiability of general risk functionals and its application. https://arxiv.org/abs/1401.3167

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