Equilibrium controls in time inconsistent stochastic linear quadratic problems

2018/02/04 by Wang, Tianxiao
#FOS: Mathematics #Optimization and Control (math.OC)

paper · doi:10.48550/arxiv.1802.01077

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.

Related

• Characterizations of equilibrium controls in time inconsistent mean-field stochastic linear quadratic problems. I
• Time-Inconsistent Stochastic Linear--Quadratic Control
• Time-Inconsistent Mean-Field Stochastic LQ Problem: Open-Loop Time-Consistent Control
• Mixed Equilibrium Solution of Time-Inconsistent Stochastic LQ Problem
• On Time-Consistent Solution to Time-Inconsistent Linear-Quadratic Optimal Control of Discrete-Time Stochastic Systems