Optimal Brownian Stopping between radially symmetric marginals in general dimensions
Given an initial (resp., terminal) probability measure μ (resp., ν) on Rd, we characterize those optimal stopping times τ that maximize or minimize the functional E|B0−Bτ|α, α>0, where (Bt)t is Brownian motion with initial law B0∼μ and with final distribution --once stopped at τ-- equal to Bτ...
| Main Authors: | , , |
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| Format: | Journal article |
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Cornell University Library
2017
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| _version_ | 1797080419893510144 |
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| author | Ghoussoub, N Kim, Y Lim, T |
| author_facet | Ghoussoub, N Kim, Y Lim, T |
| author_sort | Ghoussoub, N |
| collection | OXFORD |
| description | Given an initial (resp., terminal) probability measure μ (resp., ν) on Rd, we characterize those optimal stopping times τ that maximize or minimize the functional E|B0−Bτ|α, α>0, where (Bt)t is Brownian motion with initial law B0∼μ and with final distribution --once stopped at τ-- equal to Bτ∼ν. The existence of such stopping times is guaranteed by Skorohod-type embeddings of probability measures in "subharmoic order" into Brownian motion. This problem is equivalent to an optimal mass transport problem with certain constraints, namely the optimal subharmonic martingale transport. Under the assumption of radial symmetry on μ and ν, we show that the optimal stopping time is a hitting time of a suitable barrier, hence is non-randomized and is unique. |
| first_indexed | 2024-03-07T00:59:46Z |
| format | Journal article |
| id | oxford-uuid:8950a7de-79af-43a0-bf83-19ba25b1f1d2 |
| institution | University of Oxford |
| last_indexed | 2024-03-07T00:59:46Z |
| publishDate | 2017 |
| publisher | Cornell University Library |
| record_format | dspace |
| spelling | oxford-uuid:8950a7de-79af-43a0-bf83-19ba25b1f1d22022-03-26T22:23:40ZOptimal Brownian Stopping between radially symmetric marginals in general dimensionsJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:8950a7de-79af-43a0-bf83-19ba25b1f1d2Symplectic Elements at OxfordCornell University Library2017Ghoussoub, NKim, YLim, TGiven an initial (resp., terminal) probability measure μ (resp., ν) on Rd, we characterize those optimal stopping times τ that maximize or minimize the functional E|B0−Bτ|α, α>0, where (Bt)t is Brownian motion with initial law B0∼μ and with final distribution --once stopped at τ-- equal to Bτ∼ν. The existence of such stopping times is guaranteed by Skorohod-type embeddings of probability measures in "subharmoic order" into Brownian motion. This problem is equivalent to an optimal mass transport problem with certain constraints, namely the optimal subharmonic martingale transport. Under the assumption of radial symmetry on μ and ν, we show that the optimal stopping time is a hitting time of a suitable barrier, hence is non-randomized and is unique. |
| spellingShingle | Ghoussoub, N Kim, Y Lim, T Optimal Brownian Stopping between radially symmetric marginals in general dimensions |
| title | Optimal Brownian Stopping between radially symmetric marginals in general dimensions |
| title_full | Optimal Brownian Stopping between radially symmetric marginals in general dimensions |
| title_fullStr | Optimal Brownian Stopping between radially symmetric marginals in general dimensions |
| title_full_unstemmed | Optimal Brownian Stopping between radially symmetric marginals in general dimensions |
| title_short | Optimal Brownian Stopping between radially symmetric marginals in general dimensions |
| title_sort | optimal brownian stopping between radially symmetric marginals in general dimensions |
| work_keys_str_mv | AT ghoussoubn optimalbrownianstoppingbetweenradiallysymmetricmarginalsingeneraldimensions AT kimy optimalbrownianstoppingbetweenradiallysymmetricmarginalsingeneraldimensions AT limt optimalbrownianstoppingbetweenradiallysymmetricmarginalsingeneraldimensions |