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Dual attainment for the martingale transport problem

Abstract:

We investigate existence of dual optimizers in one-dimensional martingale optimal transport problems. While [Ann. Probab. 45 (2017) 3038–3074] established such existence for weak (quasi-sure) duality, [Finance Stoch. 17 (2013) 477–501] showed existence for the natural stronger (pointwise) duality may fail even in regular cases. We establish that (pointwise) dual maximizers exist when y↦c(x,y) is convex, or equivalent to a convex function. It follows that when marginals are compactly supported...

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Publication status:
Published
Peer review status:
Peer reviewed
Version:
Publisher's version

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Publisher copy:
10.3150/17-BEJ1015

Authors


Beiglboeck, M More by this author
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Department:
Oxford, MPLS, Mathematical Institute
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Department:
Oxford, MPLS, Mathematical Institute
Publisher:
Bernoulli Society for Mathematical Statistics and Probability Publisher's website
Journal:
Bernoulli Journal website
Volume:
25
Issue:
3
Pages:
1640-1658
Publication date:
2019-06-12
Acceptance date:
2017-12-15
DOI:
EISSN:
1573-9759
ISSN:
1350-7265
Pubs id:
pubs:708469
URN:
uri:9795e794-893c-4217-b65c-e66f1eecf340
UUID:
uuid:9795e794-893c-4217-b65c-e66f1eecf340
Local pid:
pubs:708469

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