Indefinite mean-field type linear-quadratic stochastic optimal control problems

被引：19
|
作者：
Li, Na [1 ]
Li, Xun [2 ]
Yu, Zhiyong [3 ]
机构：
[1] Shandong Univ Finance & Econ, Sch Stat, Jinan 250014, Peoples R China
[2] Hong Kong Polytech Univ, Dept Appl Math, Hong Kong, Peoples R China
[3] Shandong Univ, Sch Math, Jinan 250100, Shandong, Peoples R China
来源：
AUTOMATICA | 2020年 / 122卷 / 122期
基金：
国家重点研发计划; 中国国家自然科学基金;
关键词：
Stochastic linear-quadratic problem; Mean-field; Hamiltonian system; Stochastic differential equation; Forward-backward stochastic differential equation; Riccati equation;
D O I：
10.1016/j.automatica.2020.109267
中图分类号：
TP [自动化技术、计算机技术];
学科分类号：
0812 ;
摘要：
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 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. (c) 2020 Elsevier Ltd. All rights reserved.
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页数：10
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