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| Type | Journal Article |
| Scope | Discipline-based scholarship |
| Title | Law-invariant functionals that collapse to the mean |
| 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 | Insurance: Mathematics and Economics |
| Publisher | Elsevier |
| Geographical Reach | international |
| ISSN | 0167-6687 |
| Volume | 98 |
| Page Range | 83 - 91 |
| Date | 2021 |
| Abstract Text | We discuss when law-invariant convex functionals "collapse to the mean". More precisely, we show that, in a large class of spaces of random variables and under mild semicontinuity assumptions, the expectation functional is, up to an affine transformation, the only law-invariant convex functional that is linear along the direction of a nonconstant random variable with nonzero expectation. This extends results obtained in the literature in a bounded setting and under additional assumptions on the functionals. We illustrate the implications of our general results for pricing rules and risk measures. |
| Free access at | Official URL |
| Official URL | https://www.sciencedirect.com/science/article/pii/S0167668721000354 |
| Digital Object Identifier | 10.1016/j.insmatheco.2021.03.002 |
| Other Identification Number | merlin-id:20872 |
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