Linear Quadratic Optimal Control Problems for Mean-Field Backward Stochastic Differential Equations

• DOI: 10.1007/s00245-017-9464-7
• Publication Date: 2017-12-07T12:58:12Z
• Authors: Xun Li; Jingrui Sun; Jie Xiong
• Keywords: Linear quadratic optimal control; 0209 industrial biotechnology; Optimality system; 02 engineering and technology; Mean-field backward stochastic differential equation; 01 natural sciences; Decoupling; 49N10, 49N35, 93E20; Riccati equation; Optimization and Control (math.OC); FOS: Mathematics; 0101 mathematics; Mathematics - Optimization and Control

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.<br/>20 pages<br/>