FROM FINITE POPULATION OPTIMAL STOPPING TO MEAN FIELD OPTIMAL STOPPING

• 成果类型: Article
• 署名作者: Talbi, Mehdi; Touzi, Nizar; Zhang, Jianfeng
• 署名单位: Universite Paris Cite; New York University; New York University Tandon School of Engineering; University of Southern California
• 刊物名称: ANNALS OF APPLIED PROBABILITY
• ISSN/ISSBN: 1050-5164
• DOI: 10.1214/24-AAP2064
• 发表日期: 2024
• 页码: 4237-4267
• 关键词: viscosity solutions; convergence problem; obstacle problems; limit theory; game limit; EQUIVALENCE; EQUATIONS; state

摘要

This paper analyzes the convergence of the finite population optimal stopping problem towards the corresponding mean field limit. Building on the viscosity solution characterization of the mean field optimal stopping problem of our previous papers ( SIAM J. Control Optim. 61 (2023) 1712-1736, 2140-2164), we prove the convergence of the value functions by adapting the Barles-Souganidis ( Asymptot. Anal. 4 (1991) 271-283) monotone scheme method to our context. We next characterize the optimal stopping policies of the mean field problem by the accumulation points of the finite population optimal stopping strategies. In particular, if the limiting problem has a unique optimal stopping policy, then the finite population optimal stopping strategies do converge towards this solution. As a by-product of our analysis, we provide an extension of the standard propagation of chaos to the context of stopped McKean-Vlasov diffusions.