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arXiv · 2209.04174

Time-inconsistent mean-field optimal stopping: A limit approach

Boualem Djehiche·Mattia Martini
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Abstract

We provide a characterization of an optimal stopping time for a class of finite horizon time-inconsistent optimal stopping problems (OSPs) of mean-field type, adapted to the Brownian filtration, including those related to mean-field diffusion processes and recursive utility functions. Despite the time-inconsistency of the OSP, we show that it is optimal to stop when the value-process hits the reward process for the first time, as is the case for the standard time-consistent OSP. We solve the problem by approximating the corresponding value-process with a sequence of Snell envelopes of processes, for which a sequence of optimal stopping times is constituted of the hitting times of each of the reward processes by the associated value-process. Then, under mild assumptions, we show that this sequence of hitting times converges in probability to the hitting time for the mean-field OSP and that the limit is optimal.

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Boualem Djehiche, Mattia Martini. 2023-07-19. Time-inconsistent mean-field optimal stopping: A limit approach. https://doi.org/10.1016/j.jmaa.2023.127582

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