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 PolytechniqueWednesday, February 22, 2023
**

**Abstract**:

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.