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arXiv · 1610.02903

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

Xun Li·Jingrui Sun·Jie Xiong
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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.

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Xun Li, Jingrui Sun, Jie Xiong. 2016-10-10. Linear Quadratic Optimal Control Problems for Mean-Field Backward Stochastic Differential Equations. https://arxiv.org/abs/1610.02903

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