The strong Fatou property of risk measures

Chen Shengzhong (), Gao Niushan () and Xanthos Foivos ()
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Chen Shengzhong: Department of Mathematics, Ryerson University,Toronto, Canada
Gao Niushan: Department of Mathematics, Ryerson University,Toronto, Canada
Xanthos Foivos: Department of Mathematics, Ryerson University,Toronto, Canada

Dependence Modeling, 2018, vol. 6, issue 1, 183-196

Abstract: In this paper, we explore several Fatou-type properties of risk measures. The paper continues to reveal that the strong Fatou property,whichwas 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 (X, L1) 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.

Keywords: Fatou property; strong Fatou property; super Fatou property; dual representations; law-invariant risk measures; surplus-invariant risk measures; inf-convolutions (search for similar items in EconPapers)
Date: 2018
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Citations: View citations in EconPapers (1)

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Persistent link: https://EconPapers.repec.org/RePEc:vrs:demode:v:6:y:2018:i:1:p:183-196:n:12

DOI: 10.1515/demo-2018-0012

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