Viscosity solutions for obstacle problems on Wasserstein space
Probability
2022-11-18 v2
Abstract
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.
Cite
@article{arxiv.2203.17162,
title = {Viscosity solutions for obstacle problems on Wasserstein space},
author = {Mehdi Talbi and Nizar Touzi and Jianfeng Zhang},
journal= {arXiv preprint arXiv:2203.17162},
year = {2022}
}
Comments
25 pages