论文标题
时间不一致的均值场最佳停止：一种极限方法
Time-inconsistent mean-field optimal stopping: A limit approach
论文作者
论文摘要
我们为一类有限的地平线时间不一致的最佳停止问题（OSP）提供了最佳停止时间的表征，该问题适合于布朗尼过滤，包括与平均场扩散过程和递归效用效用功能有关的过滤。尽管OSP具有时间弥补，但我们表明，当价值过程首次达到奖励过程时，停止是最佳的，就像标准时间一致的OSP一样。我们通过用一系列SNELL包络来近似相应的价值过程来解决问题，为此，一系列最佳停止时间构成了相关的价值过程中每个奖励过程的击球时间构成的序列。然后，在温和的假设下，我们表明，这种打击时间的序列会收敛于平均场OSP的打击时间，并且极限是最佳的。
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.
