2018
DOI: 10.1007/s00245-018-9513-x
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Equilibrium Controls in Time Inconsistent Stochastic Linear Quadratic Problems

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 unif ied manners. These results indicate clearer and deeper distinctions among these notions. For example, in particular time consistent setting, the openloop equilibrium controls are fully characterized by f irst-order, sec… Show more

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Cited by 29 publications
(26 citation statements)
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“…For the proof of uniqueness of open-loop equilibrium controls, our result extends the counterparts in [8], and our procedures are different from theirs as well. We emphasize that the characterization viewpoint on time inconsistent stochastic linear quadratic problem were also used in other specific/different frameworks, such as [4], [8], [9], [12], [14]. At last, by our study we also find the following interesting facts:…”
Section: Introductionsupporting
confidence: 62%
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“…For the proof of uniqueness of open-loop equilibrium controls, our result extends the counterparts in [8], and our procedures are different from theirs as well. We emphasize that the characterization viewpoint on time inconsistent stochastic linear quadratic problem were also used in other specific/different frameworks, such as [4], [8], [9], [12], [14]. At last, by our study we also find the following interesting facts:…”
Section: Introductionsupporting
confidence: 62%
“…Remark 3.8. If the mean-field terms in the state equation disappears, Theorem 3.1 reduces to the counterparts in [14]. If moreover R, Q = 0, Q, R, G are definite, then (3.33) is obvious to see, and Theorem 3.1 becomes consistent with Theorem 3.5 in [8].…”
Section: To Our Best the Conclusion Of Lemma 33 Is New In The Litermentioning
confidence: 82%
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“…This can be characterized by solving the HJB equation obtained by discretizing the corresponding optimal control problem, which is closely related to the multiperson differential game [2], [3], [8], [9], [14]- [18], [24], [35], [36]. In addition, the mixed equilibrium solution concept was used in [37], and the Markovian framework for timeinconsistent linear-quadratic problems was developed in [38].…”
Section: Introductionmentioning
confidence: 99%