Automatic Fatou property of law-invariant risk measures

Shengzhong Chen, Niushan Gao, Denny H. Leung and Lei Li

Insurance: Mathematics and Economics, 2022, vol. 105, issue C, 41-53

Abstract: In the paper we investigate automatic Fatou property of law-invariant risk measures on a rearrangement-invariant function space X other than L∞. The main result is the following characterization: Every real-valued, law-invariant, coherent risk measure on X has the Fatou property at every random variable X∈X whose negative tails have vanishing norm (i.e., limn⁡‖X1{X≤−n}‖=0) if and only if X satisfies the Almost Order Continuous Equidistributional Average (AOCEA) property, namely, d(CL(X),Xa)=0 for any X∈X+, where CL(X) is the convex hull of all random variables having the same distribution as X and Xa={X∈X:limn⁡‖X1{|X|≥n}‖=0}. As a consequence, we show that under the AOCEA property, every real-valued, law-invariant, coherent risk measure on X admits a tractable dual representation at every X∈X whose negative tails have vanishing norm. Furthermore, we show that the AOCEA property is satisfied by most classical model spaces, including Orlicz spaces, and therefore the foregoing results have wide applications.

Keywords: Automatic Fatou property; Automatic continuity; Automatic dual representation; Law invariance; Risk measures (search for similar items in EconPapers)
JEL-codes: C65 G10 (search for similar items in EconPapers)
Date: 2022
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Citations: View citations in EconPapers (1)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:insuma:v:105:y:2022:i:c:p:41-53

DOI: 10.1016/j.insmatheco.2022.03.007

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