Work

From finite population optimal stopping to mean field optimal stopping

Year: 2024

Type: article

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 (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.

Source: The Annals of Applied Probability

DOI: 10.1214/24-aap2064

Authors: Mehdi Talbi, Nizar Touzi, Jianfeng Zhang

Institutions: Université Paris Cité, Laboratoire de Probabilités, Statistique et Modélisation, New York University, University of Southern California

Language: English

Topic: Stochastic processes and financial applications

Subfield: Finance

Field: Economics, Econometrics and Finance

Domain: Social Sciences

Open Access status: green

Funder: National Science Foundation

Awards: Dynamical Approaches for Some Complex Stochastic Systems, Stochastic Analysis and Numerics for Large Scale Dynamical Systems, with Applications