Constrained Optimal Transport

Abstract

The classical duality theory of Kantorovich and Kellerer for the classical optimal transport is generalized to an abstract framework and a characterization of the dual elements is provided. This abstract generalization is set in a Banach lattice $\mathcal{X}$ with a order unit. The primal problem is given as the supremum over a convex subset of the positive unit sphere of the topological dual of $\mathcal{X}$ and the dual problem is defined on the bi-dual of $\mathcal{X}$. These results are then applied to several extensions of the classical optimal transport.

References in corpus (2)

• A stochastic control approach to no-arbitrage bounds given marginals, with an application to lookback options
• Duality for increasing convex functionals with countably many marginal constraints

Cited by in corpus (2)

• Martingale optimal transport duality
• Path constrained unbalanced optimal transport