A note on continuity and asymptotic consistency of measures of risk and variability
Abstract
In this short note, we show that every convex, order bounded above functional on a Frechet lattice is automatically norm continuous. This improves a result in \cite{RS06} and applies to many deviation and variability measures. We also show that an order-continuous, law-invariant functional on an Orlicz space is strongly consistent everywhere, extending a result in \cite{KSZ14}.
- Publication:
-
arXiv e-prints
- Pub Date:
- May 2024
- DOI:
- 10.48550/arXiv.2405.09766
- arXiv:
- arXiv:2405.09766
- Bibcode:
- 2024arXiv240509766G
- Keywords:
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- Quantitative Finance - Risk Management;
- 91G70;
- 91B30;
- 46E30