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Structure of optimal martingale transport plans in general dimensions

Abstract:

Given two probability measures μ and ν in “convex order” on Rd, we study the profile of one-step martingale plans π on Rd×Rd that optimize the expected value of the modulus of their increment among all martingales having μ and ν as marginals. While there is a great deal of results for the real line (i.e., when d=1), much less is known in the richer and more delicate higher-dimensional case that we tackle in this paper. We show that many structural results can be obtained, provided the initial...

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Publication status:
Published
Peer review status:
Peer reviewed

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Publisher copy:
10.1214/18-AOP1258

Authors


Ghoussoub, N More by this author
More by this author
Institution:
University of Oxford
Division:
MPLS Division
Department:
Mathematical Institute
Publisher:
Institute of Mathematical Statistics Publisher's website
Journal:
Annals of Probability Journal website
Volume:
47
Issue:
1
Pages:
109-164
Publication date:
2018-12-13
Acceptance date:
2018-02-11
DOI:
EISSN:
2168-894X
ISSN:
0091-1798
Pubs id:
pubs:686290
URN:
uri:86813f0d-2899-451f-96a7-c66786033820
UUID:
uuid:86813f0d-2899-451f-96a7-c66786033820
Local pid:
pubs:686290

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