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

被引：2
|
作者：
Xun Li
Jingrui Sun
Jie Xiong
机构：
[1] The Hong Kong Polytechnic University,Department of Applied Mathematics
[2] National University of Singapore,Department of Mathematics
[3] University of Macau,Department of Mathematics
[4] South University of Science and Technology of China,Department of Mathematics
来源：
Applied Mathematics & Optimization | 2019年 / 80卷
关键词：
Linear quadratic optimal control; Mean-field backward stochastic differential equation; Riccati equation; Optimality system; Decoupling; 49N10; 49N35; 93E20;
D O I：
暂无
中图分类号：
学科分类号：
摘要：
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.
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页码：223 / 250
页数：27
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