论文标题
不确定的平均场型线性季节随机最佳控制问题
Indefinite Mean-Field Type Linear-Quadratic Stochastic Optimal Control Problems
论文作者
论文摘要
本文重点介绍了无限的随机平均场线性季度（对于短）最佳控制问题，这允许状态和控制成本功能的加权矩阵无限期。随机哈密顿系统和riccati方程的可溶性均在正定情况和不确定的情况下提出。分别获得开环形式和闭环形式的最佳控件。此外，可以在不确定的MF-LQ问题的框架内解决动态均值变化问题。其他两个例子阐明了建立的理论结果。
This paper focuses on indefinite stochastic mean-field linear-quadratic (MF-LQ, for short) optimal control problems, which allow the weighting matrices for state and control in the cost functional to be indefinite. The solvability of stochastic Hamiltonian system and Riccati equations is presented under both positive definite case and indefinite case. The optimal controls in open-loop form and closed-loop form are obtained, respectively. Moreover, the dynamic mean-variance problem can be solved within the framework of the indefinite MF-LQ problem. Other two examples shed light on the theoretical results established.
