{"paper":{"title":"Optimal Brownian Stopping between radially symmetric marginals in general dimensions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.OC","q-fin.MF"],"primary_cat":"math.PR","authors_text":"Nassif Ghoussoub, Tongseok Lim, Young-Heon Kim","submitted_at":"2017-11-08T01:13:29Z","abstract_excerpt":"Given an initial (resp., terminal) probability measure $\\mu$ (resp., $\\nu$) on $\\mathbb{R}^d$, we characterize those optimal stopping times $\\tau$ that maximize or minimize the functional $\\mathbb{E} |B_0 - B_\\tau|^{\\alpha}$, $\\alpha > 0$, where $(B_t)_t$ is Brownian motion with initial law $B_0\\sim \\mu$ and with final distribution --once stopped at $\\tau$-- equal to $B_\\tau\\sim \\nu$.\n  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"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1711.02784","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}