This was part of Distributed Solutions to Complex Societal Problems Reunion Workshop
Stochastic optimal transport and HJB equations on the set of probability measures
Charles Bertucci, Ecole Polytechnique
Wednesday, February 22, 2023
I will introduce a new variant of the optimal transport problem in which the target measure is stochastic. I will show that, under suitable assumptions on the target process, the value of this problem satisfies a HJB equation on the set of probability measures. I will then give a general comparison principle for such type of equations and prove how we can characterize the value of such a problem by means of the theory of viscosity solutions.