Backward martingale transport and Fitzpatrick functions in pseudo-Euclidean spaces
We study an optimal transport problem with a backward martingale constraint in a pseudo-Euclidean space S. We show that the dual problem consists in the minimization of the expected values of the Fitzpatrick functions associated with maximal S-monotone sets. An optimal plan γ and an optimal maximal...
| Главные авторы: | , |
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| Формат: | Journal article |
| Язык: | English |
| Опубликовано: |
Institute of Mathematical Statistics
2024
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| _version_ | 1826312034013151232 |
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| author | Kramkov, D Sîrbu, M |
| author_facet | Kramkov, D Sîrbu, M |
| author_sort | Kramkov, D |
| collection | OXFORD |
| description | We study an optimal transport problem with a backward martingale constraint in a pseudo-Euclidean space S. We show that the dual problem consists in the minimization of the expected values of the Fitzpatrick functions associated with maximal S-monotone sets. An optimal plan γ and an optimal maximal S-monotone set G are characterized by the condition that the support of γ is contained in the graph of the S-projection on G. For a Gaussian random variable Y, we get a unique decomposition:
Y
=
X
+
Z
, where X and Z are independent Gaussian random variables taking values, respectively, in complementary positive and negative linear subspaces of the S-space. |
| first_indexed | 2024-03-07T08:21:38Z |
| format | Journal article |
| id | oxford-uuid:6ac0c56d-0c37-42b9-aad9-f89c8a34eb96 |
| institution | University of Oxford |
| language | English |
| last_indexed | 2024-03-07T08:21:38Z |
| publishDate | 2024 |
| publisher | Institute of Mathematical Statistics |
| record_format | dspace |
| spelling | oxford-uuid:6ac0c56d-0c37-42b9-aad9-f89c8a34eb962024-02-05T09:55:08ZBackward martingale transport and Fitzpatrick functions in pseudo-Euclidean spacesJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:6ac0c56d-0c37-42b9-aad9-f89c8a34eb96EnglishSymplectic ElementsInstitute of Mathematical Statistics2024Kramkov, DSîrbu, MWe study an optimal transport problem with a backward martingale constraint in a pseudo-Euclidean space S. We show that the dual problem consists in the minimization of the expected values of the Fitzpatrick functions associated with maximal S-monotone sets. An optimal plan γ and an optimal maximal S-monotone set G are characterized by the condition that the support of γ is contained in the graph of the S-projection on G. For a Gaussian random variable Y, we get a unique decomposition: Y = X + Z , where X and Z are independent Gaussian random variables taking values, respectively, in complementary positive and negative linear subspaces of the S-space. |
| spellingShingle | Kramkov, D Sîrbu, M Backward martingale transport and Fitzpatrick functions in pseudo-Euclidean spaces |
| title | Backward martingale transport and Fitzpatrick functions in pseudo-Euclidean spaces |
| title_full | Backward martingale transport and Fitzpatrick functions in pseudo-Euclidean spaces |
| title_fullStr | Backward martingale transport and Fitzpatrick functions in pseudo-Euclidean spaces |
| title_full_unstemmed | Backward martingale transport and Fitzpatrick functions in pseudo-Euclidean spaces |
| title_short | Backward martingale transport and Fitzpatrick functions in pseudo-Euclidean spaces |
| title_sort | backward martingale transport and fitzpatrick functions in pseudo euclidean spaces |
| work_keys_str_mv | AT kramkovd backwardmartingaletransportandfitzpatrickfunctionsinpseudoeuclideanspaces AT sirbum backwardmartingaletransportandfitzpatrickfunctionsinpseudoeuclideanspaces |