{"ID":2891818,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2507.16582","arxiv_id":"2507.16582","title":"Mean-Field Stochastic Linear-Quadratic Optimal Controls: Roles of Expectation and Conditional Expectation Operators","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, naïve, 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.","short_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, naïve, and equilibrium solutions and establish the well-posedness of the associated Riccati e...","url_abs":"https://arxiv.org/abs/2507.16582","url_pdf":"https://arxiv.org/pdf/2507.16582v1","authors":"[\"Hanxiao Wang\",\"Jiongmin Yong\"]","published":"2025-07-22T13:34:44Z","proceeding":"math.OC","tasks":"[\"math.OC\"]","methods":"[]","has_code":false}