关于风险和变异性测量的连续性和一致性的说明

arXiv - QuantFin - Risk Management Pub Date : 2024-05-16 DOI:arxiv-2405.09766

Niushan Gao, Foivos Xanthos

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引用次数: 0

摘要

在这篇短文中，我们证明了巴拿赫网格上每一个凸的、有阶有界的上面函数都是自动规范连续的。这改进了（cite{RS06}）中的一个结果，并适用于许多偏差和变异度量。我们还证明了奥利奇空间上的阶连续、律不变函数在任何地方都是强一致的，这扩展了（cite{KSZ14}中的一个结果。

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

In this short note, we show that every convex, order bounded above functional on a Banach 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}.

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arXiv - QuantFin - Risk Management

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