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Linear-quadratic optimal control problems for mean-field stochastic differential equations -- time-consistent solutions


Author: Jiongmin Yong
Journal: Trans. Amer. Math. Soc.
MSC (2010): Primary 93E20, 49N10; Secondary 49N70
DOI: https://doi.org/10.1090/tran/6502
Published electronically: December 18, 2015
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Abstract: Linear-quadratic optimal control problems are considered for
mean-field stochastic differential equations with deterministic coefficients.
Time-inconsistency feature of the problems is carefully investigated. Both open-loop and closed-loop equilibrium solutions are presented for such kinds of problems. Open-loop solutions are presented by means of the variational method with decoupling of forward-backward stochastic differential equations, which leads to a Riccati equation system lack of symmetry. Closed-loop solutions are presented by means of multi-person differential games, the limit of which leads to a Riccati equation system with a symmetric structure.


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Additional Information

Jiongmin Yong
Affiliation: Department of Mathematics, University of Central Florida, Orlando, Florida 32816
Email: jiongmin.yong@ucf.edu

DOI: https://doi.org/10.1090/tran/6502
Keywords: Mean-field stochastic differential equation, linear-quadratic optimal control, time-inconsistency, equilibrium solution, Riccati equation, Lyapunov equation, $N$-person differential games
Received by editor(s): May 6, 2013
Received by editor(s) in revised form: June 13, 2014, and August 28, 2015
Published electronically: December 18, 2015
Additional Notes: This work was supported in part by NSF Grant DMS-1406776.
Article copyright: © Copyright 2015 American Mathematical Society