Linear Quadratic Optimal Control Problems for Mean-Field Backward Stochastic Differential Equations
Optimization and Control
2016-10-11 v1
Abstract
This paper is concerned with linear quadratic optimal control problems for mean-field backward stochastic differential equations (MF-BSDEs, for short) with deterministic coefficients. The optimality system, which is a linear mean-field forward-backward stochastic differential equation with constraint, is obtained by a variational method. By decoupling the optimality system, two coupled Riccati equations and an MF-BSDE are derived. It turns out that the coupled two Riccati equations are uniquely solvable. Then a complete and explicit representation is obtained for the optimal control.
Cite
@article{arxiv.1610.02903,
title = {Linear Quadratic Optimal Control Problems for Mean-Field Backward Stochastic Differential Equations},
author = {Xun Li and Jingrui Sun and Jie Xiong},
journal= {arXiv preprint arXiv:1610.02903},
year = {2016}
}
Comments
20 pages