A note on continuity and asymptotic consistency of measures of risk and variability
Risk Management
2025-01-29 v2
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}.
Cite
@article{arxiv.2405.09766,
title = {A note on continuity and asymptotic consistency of measures of risk and variability},
author = {Niushan Gao and Foivos Xanthos},
journal= {arXiv preprint arXiv:2405.09766},
year = {2025}
}