Quasi-Hadamard differentiability of general risk functionals and its application
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
Cite
@article{arxiv.1401.3167,
title = {Quasi-Hadamard differentiability of general risk functionals and its application},
author = {Volker Krätschmer and Alexander Schied and Henryk Zähle},
journal= {arXiv preprint arXiv:1401.3167},
year = {2015}
}