A note on continuity and asymptotic consistency of measures of risk and variability
arXiv:2405.09766 · doi:10.1017/asb.2024.33
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}.