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Type | Journal Article |
Scope | Discipline-based scholarship |
Title | Fatou property, representations, and extensions of law-invariant risk measures on general Orlicz spaces |
Organization Unit | |
Authors |
|
Item Subtype | Original Work |
Refereed | Yes |
Status | Published in final form |
Language |
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Journal Title | Finance and Stochastics |
Publisher | Springer |
Geographical Reach | international |
ISSN | 0949-2984 |
Volume | 22 |
Number | 2 |
Page Range | 395 - 415 |
Date | 2018 |
Abstract Text | 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. |
Related URLs | |
Digital Object Identifier | 10.1007/s00780-018-0357-7 |
Other Identification Number | merlin-id:16301 |
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