Mean-Field Stochastic Linear-Quadratic Optimal Controls: Roles of Expectation and Conditional Expectation Operators
Optimization and Control
2025-07-23 v1
Abstract
This paper investigates a mean-field linear-quadratic optimal control problem where the state dynamics and cost functional incorporate both expectation and conditional expectation terms. We explicitly derive the pre-committed, na\"{\i}ve, and equilibrium solutions and establish the well-posedness of the associated Riccati equations. This reveals how the expectation and conditional expectation operators influence time-consistency.
Keywords
Cite
@article{arxiv.2507.16582,
title = {Mean-Field Stochastic Linear-Quadratic Optimal Controls: Roles of Expectation and Conditional Expectation Operators},
author = {Hanxiao Wang and Jiongmin Yong},
journal= {arXiv preprint arXiv:2507.16582},
year = {2025}
}