Stochastic optimal transport and HJB equations on the set of probability measures
Charles Bertucci, Ecole Polytechnique
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.