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We propose a modified primal-dual method for general convex optimization problems with changing constraints. We obtain properties of Lagrangian saddle points for these problems which enable us to establish convergence of the proposed…
In the first part of the paper we briefly decribe the classical problem, raised by Monge in 1781, of optimal transportation of mass. We discuss also Kantorovich's weak solution of the problem, which leads to general existence results, to a…
The aim of this notes is to give a concise introduction to control theory for systems governed by stochastic partial differential equations. We shall mainly focus on controllability and optimal control problems for these systems. For the…
We investigate duality and existence of dual optimizers for several adapted optimal transport problems under minimal assumptions. This includes the causal and bicausal transport, the causal and bicausal barycenter problem, and a…
The manipulation of a collection of fluid particles in a low Reynolds number environment has several important applications. As we demonstrate in this paper, this manipulation problem is related to the scientific question of how fluid flow…
We study a multi-marginal optimal transportation problem. Under certain conditions on the cost function and the first marginal, we prove that the solution to the relaxed, Kantorovich version of the problem induces a solution to the Monge…
We consider the Monge problem of optimal transport between a compactly supported source measure and a target probability measure with unbounded support. We consider the convergence of optimal maps and potential functions when the target…
We prove that $c$-cyclically monotone transport plans $\pi$ optimize the Monge-Kantorovich transportation problem under an additional measurability condition. This measurability condition is always satisfied for finitely valued, lower…
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…
Motivated by recent developments in the calibration of stochastic volatility models (SVMs for short), we study continuous-time formulations of martingale optimal transport and martingale Schr\"odinger bridge problems. We establish duality…
The aim of this article is to show that the Monge-Kantorovich problem is the limit of a sequence of entropy minimization problems when a fluctuation parameter tends down to zero. We prove the convergence of the entropic values to the…
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 study a generic principal-agent problem in continuous time on a finite time horizon. We introduce a framework in which the agent is allowed to employ measure-valued controls and characterise the continuation utility as a solution to a…
A novel methodology is developed for the solution of the data-driven Monge optimal transport barycenter problem, where the pushforward condition is formulated in terms of the statistical independence between two sets of random variables:…
We consider an optimal transport problem between laws of random probability measures: given a base cost function, we build the associated OT cost between probability measures that in turn we use to define the OT cost between probability…
In this article we prove the existence of a stochastic optimal transference plan for a stochastic Monge-Kantorovich problem by measurable selection theorem. A stochastic version of Kantorovich duality and the characterization of stochastic…
We study a stochastic control problem for continuous multidimensional martingales with fixed quadratic variation. In a radially symmetric environment, we are able to find an explicit solution to the control problem and find an optimal…
We consider a stochastic transportation problem between two prescribed probability distributions (a source and a target) over processes with general drift dependence and with free end times. First, and in order to establish a dual…
The Monge-Kantorovich problem is revisited by means of a variant of the saddle-point method without appealing to $c$-conjugates. A new abstract characterization of the optimal plans is obtained in the case where the cost function takes…
We analyze conditional optimization problems arising in discrete time Principal-Agent problems of delegated portfolio optimization with linear contracts. Applying tools from Conditional Analysis we show that some results known in the…