Sensitivity of functionals of McKean-Vlasov SDE's with respect to the initial distribution
We examine the sensitivity at the origin of the distributional robust optimization problem in the context of a model generated by a mean field stochastic differential equation. We adapt the finite dimensional argument developed by Bartl, Drapeau, Obloj \& Wiesel to our framework involving the in...
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| creator | de Feo, Filippo Federico, Salvatore Gozzi, Fausto Touzi, Nizar |
| description | We examine the sensitivity at the origin of the distributional robust
optimization problem in the context of a model generated by a mean field
stochastic differential equation. We adapt the finite dimensional argument
developed by Bartl, Drapeau, Obloj \& Wiesel to our framework involving the
infinite dimensional gradient of the solution of the mean field SDE with
respect to its initial data. We revisit the derivation of this gradient process
as previously introduced by Buckdahn, Li \& Peng, and we complement the
existing properties so as to satisfy the requirement of our main result. |
| doi_str_mv | 10.48550/arxiv.2412.15906 |
| format | Article |
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optimization problem in the context of a model generated by a mean field
stochastic differential equation. We adapt the finite dimensional argument
developed by Bartl, Drapeau, Obloj \& Wiesel to our framework involving the
infinite dimensional gradient of the solution of the mean field SDE with
respect to its initial data. We revisit the derivation of this gradient process
as previously introduced by Buckdahn, Li \& Peng, and we complement the
existing properties so as to satisfy the requirement of our main result.</description><identifier>DOI: 10.48550/arxiv.2412.15906</identifier><language>eng</language><subject>Mathematics - Probability</subject><creationdate>2024-12</creationdate><rights>http://arxiv.org/licenses/nonexclusive-distrib/1.0</rights><oa>free_for_read</oa><woscitedreferencessubscribed>false</woscitedreferencessubscribed></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><link.rule.ids>228,230,776,881</link.rule.ids><linktorsrc>$$Uhttps://arxiv.org/abs/2412.15906$$EView_record_in_Cornell_University$$FView_record_in_$$GCornell_University$$Hfree_for_read</linktorsrc><backlink>$$Uhttps://doi.org/10.48550/arXiv.2412.15906$$DView paper in arXiv$$Hfree_for_read</backlink></links><search><creatorcontrib>de Feo, Filippo</creatorcontrib><creatorcontrib>Federico, Salvatore</creatorcontrib><creatorcontrib>Gozzi, Fausto</creatorcontrib><creatorcontrib>Touzi, Nizar</creatorcontrib><title>Sensitivity of functionals of McKean-Vlasov SDE's with respect to the initial distribution</title><description>We examine the sensitivity at the origin of the distributional robust
optimization problem in the context of a model generated by a mean field
stochastic differential equation. We adapt the finite dimensional argument
developed by Bartl, Drapeau, Obloj \& Wiesel to our framework involving the
infinite dimensional gradient of the solution of the mean field SDE with
respect to its initial data. We revisit the derivation of this gradient process
as previously introduced by Buckdahn, Li \& Peng, and we complement the
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optimization problem in the context of a model generated by a mean field
stochastic differential equation. We adapt the finite dimensional argument
developed by Bartl, Drapeau, Obloj \& Wiesel to our framework involving the
infinite dimensional gradient of the solution of the mean field SDE with
respect to its initial data. We revisit the derivation of this gradient process
as previously introduced by Buckdahn, Li \& Peng, and we complement the
existing properties so as to satisfy the requirement of our main result.</abstract><doi>10.48550/arxiv.2412.15906</doi><oa>free_for_read</oa></addata></record> |
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| subjects | Mathematics - Probability |
| title | Sensitivity of functionals of McKean-Vlasov SDE's with respect to the initial distribution |
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