This paper presents a widely applicable approach to solving (multi-marginal, martingale)
optimal transport and related problems via neural networks. The core idea is to penalize the …

Martingale transport plans on the line are known from Beiglböck and Juillet (Ann. Probab. 44
(2016) 42–106) to have an irreducible decomposition on a (at most) countable union of …

We obtain a dual representation of the Kantorovich functional defined for functions on the
Skorokhod space using quotient sets. Our representation takes the form of a Choquet …

We introduce a constrained optimal transport problem where origins x can only be
transported to destinations y≥ x. Our statistical motivation is to describe the sharp upper …

Abstract The Skorokhod Embedding Problem is one of the classical problems in the theory
of stochastic processes, with applications in many different fields [cf. the surveys (Hobson in …

We study MinMax solution methods for a general class of optimization problems related to
(and including) optimal transport. Theoretically, the focus is on fitting a large class of …

We present a range of examples of applications of the concept of irreducible paving for pairs
of probability measures in order with respect to a lattice cone. These examples comprise …

We investigate an analogue of the irreducible convex paving in the context of generalised
convexity. Consider two $\mu,\nu $ two Radon probability measures ordered with respect to …

We consider the problem to transport resources/mass while abiding by constraints on the
flow through constrictions along their path between specified terminal distributions …

We address the problem of optimal transport with a quadratic cost functional and a constraint
on the flux through a constriction along the path. The constriction, conceptually represented …