Equilibrium controls in time inconsistent stochastic linear quadratic problems

This paper deals with a class of time inconsistent stochastic linear quadratic (SLQ) optimal control problems in Markovian framework. Three notions, i.e., closed-loop equilibrium controls/strategies, open-loop equilibrium controls and their closed-loop representations, are characterized in unified m...

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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
Equilibrium
Markov processes
Optimal control
Optimization
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Summary:This paper deals with a class of time inconsistent stochastic linear quadratic (SLQ) optimal control problems in Markovian framework. Three notions, i.e., closed-loop equilibrium controls/strategies, open-loop equilibrium controls and their closed-loop representations, are characterized in unified manners. These results indicate clearer and deeper distinctions among these notions. For example, in particular time consistent setting, the open-loop equilibrium controls are fully characterized by first-order, second-order necessary optimality conditions, and become needlessly optimal, while the closed-loop equilibrium controls naturally reduce into closed-loop optimal controls.
ISSN:2331-8422