A note on continuity and asymptotic consistency of measures of risk and variability

Niushan Gao and Foivos Xanthos

Papers from arXiv.org

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}.

Date: 2024-05, Revised 2024-10
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Published in ASTIN Bull. 55 (2025) 168-177

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