Dual attainment for the martingale transport problem

doi:10.3150/17-BEJ1015

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	Dual attainment for the martingale transport problem
	Beiglboeck, Mathias 1; Lim, Tongseok2 ; Obloj, Jan 3
	2019-08
发表期刊	BERNOULLI
ISSN	1350-7265
卷号	25 期号:3 页码:1640-1658
发表状态	已发表
DOI	10.3150/17-BEJ1015
摘要	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 (sic) c(x, y) is convex, or equivalent to a convex function. It follows that when marginals are compactly supported, the existence holds when the cost c(x, y) is twice continuously differentiable in y. Further, this may not be improved as we give examples with c(x, center dot) epsilon C2-epsilon, epsilon > 0, where dual attainment fails. Finally, when measures are compactly supported, we show that dual optimizers are Lipschitz if c is Lipschitz.
关键词	dual attainment Kantorovich duality martingale optimal transport robust mathematical finance
收录类别	SCI ; SCIE
语种	英语
资助项目	Austrian Science Foundation (FWF)[Y782]
WOS研究方向	Mathematics
WOS类目	Statistics & Probability
WOS记录号	WOS:000471192000002
出版者	INT STATISTICAL INST
WOS关键词	BOUNDS
原始文献类型	Article
引用统计
文献类型	期刊论文
条目标识符	https://kms.shanghaitech.edu.cn/handle/2MSLDSTB/48970
专题	数学科学研究所数学科学研究所_PI研究组(P)_Tongseok Lim组
通讯作者	Beiglboeck, Mathias
作者单位	1.Univ Vienna, Fac Math, Oskar Morgensternpl 1,6 Floor, A-1090 Vienna, Austria 2.ShanghaiTech Univ, Inst Math Sci, 393 Middle Huaxia Rd, Shanghai 201210, Peoples R China 3.Univ Oxford, Math Inst, Radcliffe Observ Quarter, Andrew Wiles Bldg,Woodstock Rd, Oxford OX2 6GG, England
推荐引用方式 GB/T 7714	Beiglboeck, Mathias,Lim, Tongseok,Obloj, Jan. Dual attainment for the martingale transport problem[J]. BERNOULLI,2019,25(3):1640-1658.
APA	Beiglboeck, Mathias,Lim, Tongseok,&Obloj, Jan.(2019).Dual attainment for the martingale transport problem.BERNOULLI,25(3),1640-1658.
MLA	Beiglboeck, Mathias,et al."Dual attainment for the martingale transport problem".BERNOULLI 25.3(2019):1640-1658.