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The strong Fatou property of risk measures

Shengzhong Chen, Niushan Gao and 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.

New Economics Papers: this item is included in nep-rmg
Date: 2018-05
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Handle: RePEc:arx:papers:1805.05259