@article{3ffac9a0edef4410afcd57f9ccec6381,
title = "VISCOSITY SOLUTIONS FOR OBSTACLE PROBLEMS ON WASSERSTEIN SPACE",
abstract = "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.",
keywords = "mean field optimal stopping, obstacle problems, viscosity solutions",
author = "Mehdi Talbi and Nizar Touzi and Jianfeng Zhang",
note = "Funding Information: *Received by the editors April 1, 2022; accepted for publication (in revised form) February 10, 2023; published electronically June 21, 2023. https://doi.org/10.1137/22M1488119 Funding: The first two authors received financial support from the Chaires FiME-FDD and Financial Risks of the Louis Bachelier Institute. The third author is supported in part by NSF grant DMS-1908665. \dagger CMAP, Ecole\' polytechnique, 91128 Palaiseau Cedex, France (mehdi.talbi@polytechnique.edu, nizar.touzi@polytechnique.edu). \ddagger Department of Mathematics, University of Southern California, Los Angeles, CA 90089-2532 USA (jianfenz@usc.edu). Publisher Copyright: {\textcopyright} 2023 Society for Industrial and Applied Mathematics.",
year = "2023",
doi = "10.1137/22M1488119",
language = "English (US)",
volume = "61",
pages = "1712--1736",
journal = "SIAM Journal on Control and Optimization",
issn = "0363-0129",
publisher = "Society for Industrial and Applied Mathematics Publications",
number = "3",
}