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Indefinite Mean-Field Type Linear-Quadratic Stochastic Optimal Control Problems

Abstract

This work 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 indefinite case. The optimal controls in open-loop form and closed-loop form are derived, respectively. In particular, dynamic mean-variance portfolio selection problem can be formulated as an indefinite MF-LQ problem to tackle directly. Another example also sheds light on the theoretical results established.


个人简介:李娜,教授,山东财经大学首批特聘教授,现工作于山东财经大学统计学院,主要研究方向为随机系统的最优控制与微分博弈问题。近年来,共发表论文20余篇,代表性论文发表于国际控制论三大顶级期刊SIAM Journal on Control and Optimization、Automatica、IEEE Transactions on Automatic Control等学术期刊,主持国家自然科学基金、山东省自然科学基金等项目共6项。