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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 |
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| 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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