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Mathematics > Probability

arXiv:2210.16004 (math)
[Submitted on 28 Oct 2022 (v1), last revised 29 Nov 2023 (this version, v2)]

Title:From finite population optimal stopping to mean field optimal stopping

Authors:Mehdi Talbi, Nizar Touzi, Jianfeng Zhang
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Abstract: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.
Subjects: Probability (math.PR); Optimization and Control (math.OC)
MSC classes: 60G40, 35Q89, 49N80, 49L25, 65K15
Cite as: arXiv:2210.16004 [math.PR]
  (or arXiv:2210.16004v2 [math.PR] for this version)
  https://doi.org/10.48550/arXiv.2210.16004

Submission history

From: Mehdi Talbi [view email]
[v1] Fri, 28 Oct 2022 09:10:29 UTC (42 KB)
[v2] Wed, 29 Nov 2023 11:44:51 UTC (44 KB)
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