This paper deals with a class of time inconsistent stochastic linear quadratic optimal control problems in Markovian framework. Three notions, i.e., closed-loop equilibrium strategies, open-loop equilibrium controls and open-loop equilibrium strategies, 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-ordernecessaryoptimalityconditions, and are not optimal in general, while the closed-loop equilibrium controls naturally reduce into closed-loopoptimalcontrols.

中文翻译：

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时间不一致的随机线性二次问题的平衡控制

本文研究了在马尔可夫框架中的一类时间不一致的随机线性二次最优控制问题。闭环均衡策略，开环均衡控制和开环均衡策略这三个概念以统一的方式表征。这些结果表明这些概念之间的区别更加明显和深刻。例如，在特定的时间一致的设置，开环控制平衡完全特征在于第一-顺序，第二-为了必要最优条件，而不是一般的最佳的，而闭环控制平衡自然减少到闭合-循环最优控制。