Please use this identifier to cite or link to this item: http://hdl.handle.net/10397/9575
Title: Indefinite Mean-Field Stochastic Linear-Quadratic Optimal Control
Authors: Ni, YH
Zhang, JF
Li, X 
Keywords: Indefinite stochastic linear-quadratic optimal control
Mean-field theory
Multi-period mean-variance portfolio selection
Issue Date: 2015
Publisher: Institute of Electrical and Electronics Engineers
Source: IEEE transactions on automatic control, 2015, v. 60, no. 7, p. 1786-1800 How to cite?
Journal: IEEE transactions on automatic control 
Abstract: 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.
URI: http://hdl.handle.net/10397/9575
ISSN: 0018-9286
EISSN: 1558-2523
DOI: 10.1109/TAC.2014.2385253
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