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Contribution Details
| Type | Journal Article |
| Scope | Discipline-based scholarship |
| Title | Law-invariant functionals on general spaces of random variables |
| 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 | SIAM Journal on Financial Mathematics |
| Publisher | Society for Industrial and Applied Mathematics |
| Geographical Reach | international |
| ISSN | 1945-497X |
| Volume | 12 |
| Number | 1 |
| Page Range | 318 - 341 |
| Date | 2021 |
| Abstract Text | We establish general versions of a variety of results for quasiconvex, lower-semicontinuous, and law-invariant functionals. Our results extend well-known results from the literature to a large class of spaces of random variables. We sometimes obtain sharper versions, even for the well-studied case of bounded random variables. Our approach builds on two fundamental structural results for law-invariant functionals: the equivalence of law invariance and Schur convexity, i.e., monotonicity with respect to the convex stochastic order, and the fact that a law-invariant functional is fully determined by its behavior on bounded random variables. We show how to apply these results to provide a unifying perspective on the literature on law-invariant functionals, with special emphasis on quantile-based representations, including Kusuoka representations, dilatation monotonicity, and infimal convolutions. |
| Official URL | https://epubs.siam.org/doi/10.1137/20M1341258 |
| Digital Object Identifier | 10.1137/20M1341258 |
| Other Identification Number | merlin-id:20866 |
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