Related papers: Optimal transportation under controlled stochastic…
We study the convergence of an $N$-particle Markovian controlled system to the solution of a family of stochastic McKean-Vlasov control problems, either with a finite horizon or Schr\"odinger type cost functional. Specifically, under…
It is known from clever mathematical examples \cite{Ca10} that the Monge ansatz may fail in continuous two-marginal optimal transport (alias optimal coupling alias optimal assignment) problems. Here we show that this effect already occurs…
Given a stochastic state process $(X_t)_t$ and a real-valued submartingale cost process $(S_t)_t$, we characterize optimal stopping times $\tau$ that minimize the expectation of $S_\tau$ while realizing given initial and target…
We consider the optimal transportation problem on a globally hyperbolic spacetime for some cost function $c_2$, which corresponds to the optimal transportation problem on a complete Riemannian manifold where the cost function is the…
We consider the multidimensional Monge-Kantrovich transport problem in an abstract setting. Our main results state that if a cost function and marginal measures are invariant by a family of transformations, then a solution of the Kantrovich…
Some optimization or equilibrium problems involving somehow the concept of optimal transport are presented in these notes, mainly devoted to applications to economic and game theory settings. A variant model of transport, taking into…
Consider the problem of optimally matching two measures on the circle, or equivalently two periodic measures on the real line, and suppose the cost of matching two points satisfies the Monge condition. We introduce a notion of locally…
We formulate a dynamic reinsurance problem in which the insurer seeks to control the terminal distribution of its surplus while minimizing the L2-norm of the ceded risk. Using techniques from martingale optimal transport, we show that,…
Many results in probability (most famously, Strassen's theorem on stochastic domination), characterize some relationship between probability distributions in terms of the existence of a particular structured coupling between them. Optimal…
We present a systematic study of conditional triangular transport maps in function spaces from the perspective of optimal transportation and with a view towards amortized Bayesian inference. More specifically, we develop a theory of…
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…
We present a general method, based on conjugate duality, for solving a convex minimization problem without assuming unnecessary topological restrictions on the constraint set. It leads to dual equalities and characterizations of the…
Entropic Optimal Transport (EOT), also referred to as the Schr\"odinger problem, seeks to find a random processes with prescribed initial/final marginals and with minimal relative entropy with respect to a reference measure. The relative…
We propose a scalable, distributed algorithm for the optimal transport of large-scale multi-agent systems. We formulate the problem as one of steering the collective towards a target probability measure while minimizing the total cost of…
Optimal transport has been used extensively in resource matching to promote the efficiency of resources usages by matching sources to targets. However, it requires a significant amount of computations and storage spaces for large-scale…
We establish a general condition on the cost function to obtain uniqueness and Monge solutions in the multi-marginal optimal transport problem, under the assumption that a given collection of the marginals are absolutely continuous with…
We develop a general condition on the cost function which is sufficient to imply Monge solution and uniqueness results in the multi-marginal optimal transport problem. This result unifies and generalizes several results in the rather…
This work introduces novel computational methods for entropic optimal transport (OT) problems under martingale-type conditions. The considered problems include the discrete martingale optimal transport (MOT) problem. Moreover, as the…
In this work we study a modification of the Monge-Kantorovich problem taking into account path dependence and interaction effects between particles. We prove existence of solutions under mild conditions on the data, and after imposing…
Optimal transport (OT) defines a powerful framework to compare probability distributions in a geometrically faithful way. However, the practical impact of OT is still limited because of its computational burden. We propose a new class of…