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arXiv · 1602.07825

Mean-Field Stochastic Linear Quadratic Optimal Control Problems: Closed-Loop Solvability

Xun Li·Jingrui Sun·Jiongmin Yong
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Abstract

An optimal control problem is studied for a linear mean-field stochastic differential equation with a quadratic cost functional. The coefficients and the weighting matrices in the cost functional are all assumed to be deterministic. Closed-loop strategies are introduced, which require to be independent of initial states; and such a nature makes it very useful and convenient in applications. In this paper, the existence of an optimal closed-loop strategy for the system (also called the closed-loop solvability of the problem) is characterized by the existence of a regular solution to the coupled two (generalized) Riccati equations, together with some constraints on the adapted solution to a linear backward stochastic differential equation and a linear terminal value problem of an ordinary differential equation.

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Xun Li, Jingrui Sun, Jiongmin Yong. 2016-02-25. Mean-Field Stochastic Linear Quadratic Optimal Control Problems: Closed-Loop Solvability. https://arxiv.org/abs/1602.07825

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