Author:
Backhoff-Veraguas J.,Beiglböck M.,Pammer G.
Abstract
Abstract
The optimal weak transport problem has recently been introduced by Gozlan et al. (J Funct Anal 273(11):3327–3405, 2017). We provide general existence and duality results for these problems on arbitrary Polish spaces, as well as a necessary and sufficient optimality criterion in the spirit of cyclical monotonicity. As an application we extend the Brenier–Strassen Theorem of Gozlan and Juillet (On a mixture of brenier and strassen theorems. arXiv:1808.02681, 2018) to general probability measures on $$\mathbb {R}^d$$Rd under minimal assumptions. A driving idea behind our proofs is to consider the set of transport plans with a new (‘adapted’) topology which seems better suited for the weak transport problem and allows to carry out arguments which are close to the proofs in the classical setup.
Publisher
Springer Science and Business Media LLC
Subject
Applied Mathematics,Analysis
Reference45 articles.
1. Alfonsi, A., Corbetta, J., Jourdain, B.: Sampling of probability measures in the convex order and approximation of Martingale Optimal Transport problems. arXiv e-prints, Sept (2017)
2. Alibert, J.-J., Bouchitte, G., Champion, T.: A new class of cost for optimal transport planning. hal-preprint, (2018)
3. Backhoff-Veraguas, J., Bartl, D., Beiglböck, M., Eder, M.: Adapted wasserstein distances and stability in mathematical finance. arXiv e-prints, page
arXiv:1901.07450
, Jan (2019)
4. Backhoff-Veraguas, J., Bartl, D., Beiglböck, M., Eder, M.: All adapted topologies are equal. ArXiv e-prints, page
arXiv:1905.00368
, May (2019)
5. Backhoff-Veraguas, J., Beiglböck, M., Eder, M., Pichler,A.: Fundamental properties of process distances. ArXiv e-prints, (2017)
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