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arXiv · 1805.05259

The strong Fatou property of risk measures

Shengzhong Chen·Niushan Gao·Foivos Xanthos
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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 $\mathcal{X}$ with the strong Fatou property is $\sigma(\mathcal{X},L^\infty)$ 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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Shengzhong Chen, Niushan Gao, Foivos Xanthos. 2018-05-14. The strong Fatou property of risk measures. https://arxiv.org/abs/1805.05259

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