论文标题
从有限的人口最佳停止到最佳场地最佳停止
From finite population optimal stopping to mean field optimal stopping
论文作者
论文摘要
本文分析了有限种群最佳停止问题朝相应的平均场限制的收敛性。基于粘度解决方案的表征，我们以前的论文的平均场最佳停止问题[Talbi，Touzi＆Zhang 2021＆2022]，我们通过调整Barles-Souganidis [1991]单调方案方法来证明价值函数的收敛性。接下来，我们通过有限人群最佳停止策略的积累点来表征平均场问题的最佳停止政策。特别是，如果限制问题具有独特的最佳停止政策，那么有限的人口最佳停止策略确实会趋向于该解决方案。作为我们分析的副产品，我们将混乱的标准传播扩展到停止的McKean-Vlasov扩散。
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.
