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The strong Fatou property of risk measures
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<p>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 [19], 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. </p>
Title: The strong Fatou property of risk measures
Description:
<p>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 [19], 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.
</p>.
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