On time-inconsistent extended mean-field control problems with common noise
Abstract
This paper studies a class of time-inconsistent mean field control (MFC) problems in the presence of common noise under non-exponential discount and joint law dependence of both state and control. We investigate the closed-loop time-consistent equilibrium strategies for these extended MFC problems and characterize them through an equilibrium Hamilton-Jacobi-Bellman (HJB) equation defined on the Wasserstein space. We first apply the results to the linear-quadratic (LQ) time-inconsistent MFC problems and obtain the existence of time-consistent equilibria via a comprehensive study of a nonlocal Riccati system. To illustrate the theoretical findings, two financial applications are presented. We then examine a class of non-LQ time-inconsistent MFC problems, for which we contribute the existence of time-consistent equilibria by analyzing a nonlocal nonlinear partial differential equation.
Cite
@article{arxiv.2409.07219,
title = {On time-inconsistent extended mean-field control problems with common noise},
author = {Zongxia Liang and Xiang Yu and Keyu Zhang},
journal= {arXiv preprint arXiv:2409.07219},
year = {2025}
}