Quasi-Hadamard differentiability of general risk functionals and its application
-
Volker Krätschmer
,
Alexander Schied
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.
Funding source: Deutsche Forschungsgemeinschaft
Award Identifier / Grant number: Research Training Group RTG 1953
© 2015 by De Gruyter
Artikel in diesem Heft
- Frontmatter
- Moment based estimation of supOU processes and a related stochastic volatility model
- Quasi-Hadamard differentiability of general risk functionals and its application
- Series expansions for convolutions of Pareto distributions
- A copula-based hierarchical hybrid loss distribution
Artikel in diesem Heft
- Frontmatter
- Moment based estimation of supOU processes and a related stochastic volatility model
- Quasi-Hadamard differentiability of general risk functionals and its application
- Series expansions for convolutions of Pareto distributions
- A copula-based hierarchical hybrid loss distribution
