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Indefinite Mean-Field Stochastic Linear-Quadratic Optimal Control
Ni, Yuan-Hua1,2; Zhang, Ji-Feng2; Li, Xun3
AbstractThis 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.
KeywordIndefinite stochastic linear-quadratic optimal control mean-field theory multi-period mean-variance portfolio selection
Funding ProjectNational 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 Research AreaAutomation & Control Systems ; Engineering
WOS SubjectAutomation & Control Systems ; Engineering, Electrical & Electronic
WOS IDWOS:000356871400005
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Cited Times:26[WOS]   [WOS Record]     [Related Records in WOS]
Document Type期刊论文
Affiliation1.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
Recommended Citation
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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