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Linear Constraints in Optimal Transport

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자료유형학위논문
서명/저자사항Linear Constraints in Optimal Transport.
개인저자Stebegg, Florian.
단체저자명Columbia University. Statistics.
발행사항[S.l.]: Columbia University., 2019.
발행사항Ann Arbor: ProQuest Dissertations & Theses, 2019.
형태사항284 p.
기본자료 저록Dissertations Abstracts International 81-02B.
Dissertation Abstract International
ISBN9781085688277
학위논문주기Thesis (Ph.D.)--Columbia University, 2019.
일반주기 Source: Dissertations Abstracts International, Volume: 81-02, Section: B.
Advisor: Nutz, Marcel F.
이용제한사항This item must not be sold to any third party vendors.This item must not be added to any third party search indexes.
요약This thesis studies the problem of optimal mass transportation with linear constraints -- supermartingale and martingale transport in discrete and continuous time. Appropriate versions of corresponding dual problems are introduced and shown to satisfy fundamental properties: weak duality, absence of a duality gap, and the existence of a dual optimal element. We show how the existence of a dual optimizer implies that primal optimizers can be characterized geometrically through their support -- an infinite dimensional analogue of complementary slackness. In discrete time martingale and supermartingale transport problems, we utilize this result to establish the existence of canonical transport plans, that is joint optimizers for large families of reward functions. To this end, we show that the optimal support coincides for these families. We additionally characterize these transport plans through order-theoretic minimality properties, with respect to second stochastic order and convex order, respectively, in the supermartingale and the martingale case. This characterization further shows that the canonical transport plan is unique.
일반주제명Statistics.
언어영어
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