# Linear-Quadratic Optimal Control Problems for Mean-Field Stochastic Differential Equations --- Time-Consistent Solutions

arXiv: https://arxiv.org/abs/1304.3964 · HTML: https://mlsanity.com/paper/1304.3964/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 15 Apr 2013.

## Built on by (most cited first, 1 of 1)

- [Actor-Critic Learning for Extended Mean Field Control with Deterministic Policies](https://mlsanity.com/paper/2607.11005/) (2026)

## Abstract (arXiv)

Linear-quadratic optimal control problems are considered for mean-field stochastic differential equations with deterministic coefficients. Time-inconsistency feature of the problems is carefully investigated. Both open-loop and closed-loop equilibrium solutions are presented for such kind of problems. Open-loop solutions are presented by means of variational method with decoupling of forward-backward stochastic differential equations, which lead to a Riccati equation system lack of symmetry. Closed-loop solutions are presented by means of multi-person differential games, the limit of which leads to a Riccati equation system with a symmetric structure.