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Title: Finite-horizon indefinite mean-field stochastic linear-quadratic optimal control
Authors: Ni, YH
Li, X 
Zhang, JF
Keywords: Time-inconsistency
Stochastic linear-quadratic optimal control
Forward-backward stochastic difference equation
Issue Date: 2015
Publisher: Elsevier
Source: IFAC-PapersOnLine, 2015, v. 48, no. 8, p. 211-216 How to cite?
Journal: IFAC-PapersOnLine 
Abstract: For the finite-horizon indefinite mean-field stochastic linear-quadratic optimal control problems, the open-loop optimal control and the closed-loop optimal strategy are introduced and investigated together with their characterizations, difference and relationship. The open-loop optimal control can be defined for a fixed initial state, whose existence is characterized via the solvability of a linear mean-field forward-backward stochastic difference equations with stationary conditions. Differently, the closed-loop strategy is a global notion, which involves all the initial pairs. The existence of the closed-loop optimal strategy is shown to be equivalent to the solvability of a couple of generalized difference Riccati equations, the finiteness of the value function for all the initial pairs, and the existence of open-loop optimal strategy for all the initial pairs.
Description: 17th IFAC Symposium on System Identification SYSID 2015, Beijing, October 19-21, 2015
ISSN: 2405-8963
DOI: 10.1016/j.ifacol.2015.12.127
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