Causal transference plans and their Monge-Kantorovich problems

Understand

This paper investigates causal optimal transportation problems, in the framework of two Polish spaces, both endowed with filtrations.

• Specific concretizations yield primal problems equivalent to several classical problems of stochastic control, and of stochastic calculus ; trivial filtrations yield usual problems of optimal transport.
• Within this framework, primal attainments and dual formulations are obtained, under standard hypothesis, for the related variational problems.
• These problems are intrinsically related to martingales.