Related papers: An optimal transport problem with storage fees

We study the optimal transport problem in the Euclidean space where the cost function is given by the value function associated with a Linear Quadratic minimization problem. Under appropriate assumptions, we generalize Brenier's Theorem…

Weak optimal transport generalizes the classical theory of optimal transportation to nonlinear cost functions and covers a range of problems that lie beyond the traditional theory - including entropic transport, martingale transport, and…

In this paper we present a two-stage algorithm to solve the semi-discrete Optimal Transport Problem in the case where the support of the source measure is disconnected. We establish global linear convergence and local superlinear…

We consider maps $T$ solving the optimal transport problem with a cost $c(x-y)$ modeled on the $p$-cost. For H\"older continuous marginals, we prove a $C^{1,\alpha}$-partial regularity result for $T $in the set $\{|T(x)-x|>0\}$.

The purpose of this paper is to introduce a new numerical method to solve multi-marginal optimal transport problems with pairwise interaction costs. The complexity of multi-marginal optimal transport generally scales exponentially in the…

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…

A prominent model for transportation networks is branched transport, which seeks the optimal transportation scheme to move material from a given initial to a final distribution. The cost of the scheme encodes a higher transport efficiency…

We present a flow-based approach to the optimal transport (OT) problem between two continuous distributions $\pi_0,\pi_1$ on $\mathbb{R}^d$, of minimizing a transport cost $\mathbb{E}[c(X_1-X_0)]$ in the set of couplings $(X_0,X_1)$ whose…

Discrete optimal transportation problems arise in various contexts in engineering, the sciences and the social sciences. Often the underlying cost criterion is unknown, or only partly known, and the observed optimal solutions are corrupted…

We study an entropic optimal transport problem in which the transport plan is penalized by a nonlinear convex functional acting on the coupling. We establish existence, uniqueness, and uniform a priori bounds for minimizers, and we show…

We consider the simultaneous optimal transportation of measures, where the target marginal is not necessarily fixed. For this problem, we prove the existence of a solution for completely regular spaces and investigate the structure of the…

We study multi-marginal optimal transport problems from a probabilistic graphical model perspective. We point out an elegant connection between the two when the underlying cost for optimal transport allows a graph structure. In particular,…

The duality between the robust (or equivalently, model independent) hedging of path dependent European options and a martingale optimal transport problem is proved. The financial market is modeled through a risky asset whose price is only…

In this paper, we prove a structure theorem for discrete optimal transportation plans. We show that, given any pair of discrete probability measures and a cost function, there exists an optimal transportation plan that can be expressed as…

We consider robust pricing and hedging for options written on multiple assets given market option prices for the individual assets. The resulting problem is called the multi-marginal martingale optimal transport problem. We propose two…

In this paper we study the class of optimal entropy-transport problems introduced by Liero, Mielke and Savar\'e in Inventiones Mathematicae 211 in 2018. This class of unbalanced transport metrics allows for transport between measures of…

We prove existence and uniqueness of solutions for a system of PDEs which describes the growth of a sandpile in a silos with flat bottom under the action of a vertical, measure source. The tools we use are a discrete approximation of the…

We consider a class of stochastic optimal transport, SOT for short, with given two endpoint marginals in the case where a cost function exhibits at most quadratic growth. We first study the upper and lower estimates, the short--time…

Transferring a physical system from an initial to a final state while minimizing energetic losses is an interdisciplinary control problem that bridges stochastic thermodynamics and optimal transport theory. Recent research typically…

For a finite metric graph $X=(V,E,\ell)$, where $V$ is endowed with the shortest path metric, we consider the transportation cost problem associated with the distance $d$ on $V$. Namely, for $f$ a function with total sum 0 on $V$, write…