Viscosity solutions for obstacle problems on Wasserstein space

Mehdi Talbi, Nizar Touzi, Jianfeng Zhang

Published 2022-03-31Version 1

This paper is a continuation of our accompanying paper [Talbi, Touzi and Zhang (2021)], where we characterized the mean field optimal stopping problem by an obstacle equation on the Wasserstein space of probability measures, provided that the value function is smooth. Our purpose here is to establish this characterization under weaker regularity requirements. We shall define a notion of viscosity solutions for such equation, and prove existence, stability, and comparison principle.