The strong Fatou property of risk measures

2018/05/14 by Shengzhong Chen, Chen, Shengzhong, Niushan Gao +3 · 2 citations
Decision Sciences · #FOS: Economics and business #Risk Management (q-fin.RM) #Risk and Portfolio Optimization

paper · pdf · doi:10.48550/arxiv.1805.05259

openalex publication_date 2018/05/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper, we explore several Fatou-type properties of risk measures. The paper continues to reveal that the strong Fatou property, which was introduced in [17], seems to be most suitable to ensure nice dual representations of risk measures. Our main result asserts that every quasiconvex law-invariant functional on a rearrangement invariant space X with the strong Fatou property is σ(X,L^∞) lower semicontinuous and that the converse is true on a wide range of rearrangement invariant spaces. We also study inf-convolutions of law-invariant or surplus-invariant risk measures that preserve the (strong) Fatou property.

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