VISCOSITY SOLUTIONS FOR OBSTACLE PROBLEMS ON WASSERSTEIN SPACE

被引：7
作者：
Talbi, Mehdi [1 ]
Touzi, Nizar [1 ]
Zhang, Jianfeng [2 ]
机构：
[1] Ecole Polytech, CMAP, F-91128 Palaiseau, France
[2] Univ Southern Calif, Dept Math, Los Angeles, CA 90089 USA
来源：
SIAM JOURNAL ON CONTROL AND OPTIMIZATION | 2023年 / 61卷 / 03期
关键词：
mean field optimal stopping; obstacle problems; viscosity solutions; NONLINEAR 2ND-ORDER EQUATIONS; OPTIMAL STOCHASTIC-CONTROL; INFINITE DIMENSIONS;
D O I：
10.1137/22M1488119
中图分类号：
TP [自动化技术、计算机技术];
学科分类号：
0812 ;
摘要：
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.
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页码：1712 / 1736
页数：25
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