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arXiv · 2302.03300

A mean-field version of Bank-El Karoui's representation of stochastic processes

Xihao He·Xiaolu Tan·Jun Zou
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Abstract

We study a mean-field version of Bank-El Karoui's representation theorem of stochastic processes. Under different technical conditions, we establish some existence and uniqueness results. As motivation and first applications, our mean-field representation results provide a unified approach to study different Mean-Field Games (MFGs) in the setting with common noise and multiple populations, including the MFG of timing, the MFG with singular control, etc. As a crucial technical step, we provide a stability result on the classical Bank-El Karoui's representation theorem, which has its own interests and other applications, such as in deriving stability results of the optimizers (in the strong sense) for a class of optimal stopping problems and singular control problems.

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Xihao He, Xiaolu Tan, Jun Zou. 2023-02-07. A mean-field version of Bank-El Karoui's representation of stochastic processes. https://arxiv.org/abs/2302.03300

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