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Existence, Duality, and Cyclical monotonicity for weak transport costs
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In this paper, the authors provide general existence and duality results for weak transport problems on arbitrary Polish spaces, as well as a necessary and sufficient optimality criterion in the spirit of cyclical monotonicity.Abstract:
The optimal weak transport problem has recently been introduced by Gozlan et.\ al. 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-Juillet to general probability measures on $R^d$ 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.read more
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Adapted Wasserstein Distances and Stability in Mathematical Finance
TL;DR: In this paper, a suitable adapted version of the Wasserstein distance is proposed, which takes the temporal structure of pricing models into account, which allows to establish Lipschitz properties of hedging strategies for semimartingale models in discrete and continuous time.
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On a mixture of brenier and strassen theorems
Nathael Gozlan,Nicolas Juillet +1 more
TL;DR: In this paper, the authors give a characterization of optimal transport plans for a variant of the usual quadratic transport cost introduced in [33], where the optimal plans are composition of a deterministic transport given by the gradient of a continuously differentiable convex function followed by a martingale coupling.
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Stability of martingale optimal transport and weak optimal transport.
TL;DR: In this paper, the authors give a positive answer and establish stability of the martingale transport problem, and they also apply to the weak transport problem introduced by Gozlan, Roberto, Samson and Tetali.
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Estimating processes in adapted Wasserstein distance
TL;DR: This article aims to construct an adapted variant of the empirical measure that consistently estimates the laws of stochastic processes in full generality, and yields quantitative bounds for the convergence of the adapted empirical measure with respect to adapted Wasserstein distance.
References
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Topics in Optimal Transportation
TL;DR: In this paper, the metric side of optimal transportation is considered from a differential point of view on optimal transportation, and the Kantorovich duality of the optimal transportation problem is investigated.
Book
Classical descriptive set theory
TL;DR: In this article, the authors present a largely balanced approach, which combines many elements of the different traditions of the subject, and includes a wide variety of examples, exercises, and applications, in order to illustrate the general concepts and results of the theory.
Book
Convex analysis in general vector spaces
TL;DR: In this article, the authors present preliminary results on functional analysis and convex analysis in Locally Convex Spaces (LCS) and describe some applications of convex analyses in Normed Spaces.
Book
A weak convergence approach to the theory of large deviations
TL;DR: The Laplace Principle for the Random Walk Model with Discontinuous Statistics as mentioned in this paper has been extended to the continuous-time Markov Processes with continuous statistics, and the Laplace principle has been used for the continuous time Markov Chain model as well.