Georgia Institute of Technology College of Sciences

We study causal optimal transport problems with Markovian cost and prescribed Markovian marginal laws. We show that the associated value function solves a fully nonlinear parabolic PDE, for which we establish a comparison principle and, consequently, uniqueness of its viscosity solution. This PDE characterization allows us to identify the value with that of a constrained version of the control problem for the Kushner–Stratonovich equation. We also obtain a third equivalent optimal control formulation with a state constraint, which leads to implementable numerical schemes for causal optimal transport. This is joint ongoing work with Julio Backhoff, Erhan Bayraktar, and Antonios Zitridis.