KMS Of Academy of mathematics and systems sciences, CAS
Indefinite Mean-Field Stochastic Linear-Quadratic Optimal Control | |
Ni, Yuan-Hua1,2; Zhang, Ji-Feng2; Li, Xun3 | |
2015-07-01 | |
发表期刊 | IEEE TRANSACTIONS ON AUTOMATIC CONTROL |
ISSN | 0018-9286 |
卷号 | 60期号:7页码:1786-1800 |
摘要 | This paper is concerned with the discrete-time indefinite mean-field linear-quadratic optimal control problem. The so-called mean-field type stochastic control problems refer to the problem of incorporating the means of the state variables into the state equations and cost functionals, such as the mean-variance portfolio selection problems. A dynamic optimization problem is called to be nonseparable in the sense of dynamic programming if it is not decomposable by a stage-wise backward recursion. The classical dynamic-programming-based optimal stochastic control methods would fail in such nonseparable situations as the principle of optimality no longer applies. In this paper, we show that both the well-posedness and the solvability of the indefinite mean-field linear-quadratic problem are equivalent to the solvability of two coupled constrained generalized difference Riccati equations and a constrained linear recursive equation. We characterize the optimal control set completely, and obtain a set of necessary and sufficient conditions on the mean-variance portfolio selection problem. The results established in this paper offer a more accurate solution scheme in tackling directly the issue of nonseparability and deriving the optimal policies analytically for the mean-variance-type portfolio selection problems. |
关键词 | Indefinite stochastic linear-quadratic optimal control mean-field theory multi-period mean-variance portfolio selection |
DOI | 10.1109/TAC.2014.2385253 |
语种 | 英语 |
资助项目 | National Natural Science Foundation of China[11471242] ; National Natural Science Foundation of China[612279002] ; China Postdoctoral Science Foundation ; China Scholarship Council ; National Key Basic Research Program of China (973 Program)[2014CB845301] ; Hong Kong RGC[520412] ; Hong Kong RGC[15209614] |
WOS研究方向 | Automation & Control Systems ; Engineering |
WOS类目 | Automation & Control Systems ; Engineering, Electrical & Electronic |
WOS记录号 | WOS:000356871400005 |
出版者 | IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC |
引用统计 | |
文献类型 | 期刊论文 |
条目标识符 | http://ir.amss.ac.cn/handle/2S8OKBNM/20114 |
专题 | 系统科学研究所 |
通讯作者 | Ni, Yuan-Hua |
作者单位 | 1.Tianjin Polytech Univ, Sch Sci, Dept Math, Tianjin 300387, Peoples R China 2.Chinese Acad Sci, Acad Math & Syst Sci, Inst Syst Sci, Key Lab Syst & Control, Beijing 100190, Peoples R China 3.Hong Kong Polytech Univ, Dept Appl Math, Kowloon, Hong Kong, Peoples R China |
推荐引用方式 GB/T 7714 | Ni, Yuan-Hua,Zhang, Ji-Feng,Li, Xun. Indefinite Mean-Field Stochastic Linear-Quadratic Optimal Control[J]. IEEE TRANSACTIONS ON AUTOMATIC CONTROL,2015,60(7):1786-1800. |
APA | Ni, Yuan-Hua,Zhang, Ji-Feng,&Li, Xun.(2015).Indefinite Mean-Field Stochastic Linear-Quadratic Optimal Control.IEEE TRANSACTIONS ON AUTOMATIC CONTROL,60(7),1786-1800. |
MLA | Ni, Yuan-Hua,et al."Indefinite Mean-Field Stochastic Linear-Quadratic Optimal Control".IEEE TRANSACTIONS ON AUTOMATIC CONTROL 60.7(2015):1786-1800. |
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