Related papers: An optimal transport problem with storage fees
A new method is proposed for the solution of the data-driven optimal transport barycenter problem and of the more general distributional barycenter problem that the article introduces. The method improves on previous approaches based on…
We provide a model-free pricing-hedging duality in continuous time. For a frictionless market consisting of $d$ risky assets with continuous price trajectories, we show that the purely analytic problem of finding the minimal superhedging…
We study a dynamic optimal transport problem on a network. Despite the cost for transport along the edges, an additional cost, scaled with a parameter $\kappa$, has to be paid for interchanging mass between edges and vertices. We show…
In this paper, we study optimal transportation problems for multifractal random measures. Since these measures are much less regular than optimal transportation theory requires, we introduce a new notion of transportation which is…
We study solutions to the multi-marginal Monge-Kantorovich problem which are concentrated on several graphs over the first marginal. We first present two general conditions on the cost function which ensure, respectively, that any solution…
We introduce a new non-linear optimal transport formulation for a pair of probability measures on $\mathbb{R}^d$ sharing a common barycentre, in which admissible transference plans satisfy two martingale-type constraints. This bi-martingale…
We propose a discrete time formulation of the semi-martingale optimal transport problem based on multi-marginal entropic transport. This approach offers a new way to formulate and solve numerically the calibration problem proposed by [17],…
We study the problem of maximizing a spectral risk measure of a given output function which depends on several underlying variables, whose individual distributions are known but whose joint distribution is not. We establish and exploit an…
We introduce an extension of the Optimal Transport problem when multiple costs are involved. Considering each cost as an agent, we aim to share equally between agents the work of transporting one distribution to another. To do so, we…
In this paper, we introduce and develop the theory of semimartingale optimal transport in a path dependent setting. Instead of the classical constraints on marginal distributions, we consider a general framework of path dependent…
This paper examines the marginal value of mobile energy storage, i.e., energy storage units that can be efficiently relocated to other locations in the power network. In particular, we formulate and analyze the joint problem for operating…
Transportation Problem is an important problem which has been widely studied in Operations Research domain. It has been often used to simulate different real life problems. In particular, application of this Problem in NP Hard Problems has…
This work establishes that an optimal transport~(OT) problem regularized by a given $f$-divergence admits the same solution as another OT problem regularized by a different $g$-divergence, under an appropriate transformation of the cost…
We study the inverse optimal transport problem of recovering the ground cost from an optimal transport plan. In discrete settings, this problem reduces to inverse linear programming and is intrinsically ill-posed, exhibiting…
In this paper we revisit a class of optimal transport problems associated to non-autonomous linear control systems. Building on properties of the cost functions on $\mathbb{R}^{d}\times\mathbb{R}^{d}$ derived from suitable variational…
The theory of Optimal Transport (OT) and Martingale Optimal Transport (MOT) were inspired by problems in economics and finance and have flourished over the past decades, making significant advances in theory and practice. MOT considers the…
In this paper we study the bicausal optimal transport problem for Markov chains, an optimal transport formulation suitable for stochastic processes which takes into consideration the accumulation of information as time evolves. Our analysis…
We introduce the von Neumann entropy regularization of Unbalanced Non-commutative Optimal Transport, specifically Non-commutative Optimal Transport between semi-definite positive matrices (not necessarily with trace one). We prove the…
Optimal transport (OT) is a powerful geometric and probabilistic tool for finding correspondences and measuring similarity between two distributions. Yet, its original formulation relies on the existence of a cost function between the…
This paper studies the geometry of the optimizer for the optimal transport problem with capacity constraints. We introduce the concept of c-capacity monotonicity, which is a generalization of c-cyclical monotonicity in optimal transport. We…