Equilibrium controls in time inconsistent stochastic linear quadratic problems
Optimization and Control
2018-02-06 v1
Abstract
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.
Cite
@article{arxiv.1802.01077,
title = {Equilibrium controls in time inconsistent stochastic linear quadratic problems},
author = {Tianxiao Wang},
journal= {arXiv preprint arXiv:1802.01077},
year = {2018}
}