Characterizations of equilibrium controls in time inconsistent mean-field stochastic linear quadratic problems. I

In this paper, a class of time inconsistent linear quadratic optimal control problems of mean-field stochastic differential equations (SDEs) is considered under Markovian framework. Open-loop equilibrium controls and their particular closed-loop representations are introduced and characterized via v...

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Bibliographic Details
Published inarXiv.org
Main Author Wang, Tianxiao
Format Paper
LanguageEnglish
Published Ithaca Cornell University Library, arXiv.org 04.02.2018
Subjects
Differential equations
Equations of state
Equilibrium
Markov analysis
Markov processes
Mathematical analysis
Optimal control
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Summary:In this paper, a class of time inconsistent linear quadratic optimal control problems of mean-field stochastic differential equations (SDEs) is considered under Markovian framework. Open-loop equilibrium controls and their particular closed-loop representations are introduced and characterized via variational ideas. Several interesting features are revealed and a system of coupled Riccati equations is derived. In contrast with the analogue optimal control problems of SDEs, the mean-field terms in state equation, which is another reason of time inconsistency, prompts us to define above two notions in new manners. An interesting result, which is almost trivial in the counterpart problems of SDEs, is given and plays significant role in the previous characterizations. As application, the uniqueness of open-loop equilibrium controls is discussed.
ISSN:2331-8422