English

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}.

Keywords

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}
}