Fatou property, representations, and extensions of law-invariant risk measures on general Orlicz spaces

Niushan Gao (), Denny Leung (), Cosimo Munari () and Foivos Xanthos ()
Additional contact information
Niushan Gao: University of Lethbridge
Denny Leung: National University of Singapore
Cosimo Munari: University of Zurich
Foivos Xanthos: Ryerson University

Finance and Stochastics, 2018, vol. 22, issue 2, No 6, 395-415

Abstract: Abstract We provide a variety of results for quasiconvex, law-invariant functionals defined on a general Orlicz space, which extend well-known results from the setting of bounded random variables. First, we show that Delbaen’s representation of convex functionals with the Fatou property, which fails in a general Orlicz space, can always be achieved under the assumption of law-invariance. Second, we identify the class of Orlicz spaces where the characterization of the Fatou property in terms of norm-lower semicontinuity by Jouini, Schachermayer and Touzi continues to hold. Third, we extend Kusuoka’s representation to a general Orlicz space. Finally, we prove a version of the extension result by Filipović and Svindland by replacing norm-lower semicontinuity with the (generally non-equivalent) Fatou property. Our results have natural applications to the theory of risk measures.

Keywords: Risk measures; Law-invariance; Fatou property; Dual representations; Conditional expectations; Orlicz spaces; 91B30; 60E05; 46E30; 46A20 (search for similar items in EconPapers)
JEL-codes: C65 G32 (search for similar items in EconPapers)
Date: 2018
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (30)

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DOI: 10.1007/s00780-018-0357-7

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