VISCOSITY SOLUTIONS FOR OBSTACLE PROBLEMS ON WASSERSTEIN SPACE.

This paper is a continuation of our accompanying paper [M. Talbi, N. Touzi, and J. Zhang, Dynamic Programming Equation for the Mean Field Optimal Stopping Problem, https://arxiv.org/abs/2103.05736, 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 an equation and prove existence, stability, and the comparison principle. [ABSTRACT FROM AUTHOR]