2022/10/28 by Mehdi Talbi, Talbi, Mehdi, Nizar Touzi +3 · 3 citations
Health Professions · Medicine · Social Sciences · #35Q89 #49L25 #49N80 #60G40 #65K15 #FOS: Mathematics #Healthcare Operations and Scheduling Optimization #Insurance, Mortality, Demography, Risk Management #Optimization and Control (math.OC) #Probability (math.PR) #Renal and Vascular Pathologies
paper · pdf · doi:10.48550/arxiv.2210.16004
openalex publication_date 2022/10/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01
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 [Talbi, Touzi & Zhang 2021 & 2022], we prove the convergence of the value functions by adapting the Barles-Souganidis [1991] 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.