A land of monotone plenty

Abstract

A fundamental concept in optimal transport is c-cyclical monotonicity: it allows to link the optimality of transport plans to the geometry of their support sets. Recently, related concepts have been successfully applied in the multi-marginal version of the transport problem as well as in the martingale transport problem which arises from model-independent finance. We establish a unifying concept of c-monotonicity / finitistic optimality which describes the geometric structure of optimizers to infinite-dimensional linear programming problems. This allows us to strengthen known results in martingale optimal transport and the infinitely marginal case of the optimal transport problem. If the optimization problem can be formulated as a multi-marginal transport problem our contribution is parallel to a recent result of Zaev.

journal version

References in corpus (2)

• The Skorokhod embedding problem and its offspring
• Martingale Inequalities and Deterministic Counterparts

Cited by in corpus (7)

• Optimal Transportation Theory with Repulsive Costs
• Causal transport in discrete time and applications
• Existence, Duality, and Cyclical monotonicity for weak transport costs
• Moments and Legendre-Fourier Series for Measures Supported on Curves
• A class of multi-marginal c-cyclically monotone sets with explicit c-splitting potentials
• Multi-marginal maximal monotonicity and convex analysis
• Decomposition of the Kantorovich problem and Wasserstein distances on simplexes