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Time-Inconsistent Stochastic LQ Problem with Regime Switching

Journal of Systems Science & Complexity 2020年第6期33卷 1733-1754页

作者： SI Binbin NI Yuan-Hua ZHANG Ji-Feng College of Artificial Intelligence Nankai UniversityTianjin 300350China Key Laboratory of IntelligentRobotics of Tianjin Tianjin 300350China Key Laboratory of Systems and control Academy of Mathematics and Systems ScienceChinese Academy ofSciencesBeijing 100190China School of Mathematical Sciences University of Chinese Academy of SciencesBeijing 100049China

This paper investigates a time-inconsistent stochastic linear-quadratic problem with regime switching that is characterized via a finite-state Markov ***-loop equilibrium control is studied in this paper whose existence is characterized via Markov-chain-modulated forward-backward stochastic difference equations and generalized Riccati-like equations with jumps.

关键词： Forward-backward stochastic difference equation open-loop equilibrium control regime switching stochastic linear-quadratic problem time inconsistency

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Time-inconsistent stochastic linear quadratic control for discrete-time systems

引用

Science China(Information Sciences) 2017年第12期60卷 44-56页

作者： Qingyuan QI Huanshui ZHANG School of control Science and Engineering Shandong University

This paper is mainly concerned with the time-inconsistent stochastic linear quadratic(LQ) control problem in a more general formulation for discrete-time systems. The time-inconsistency arises from three aspects: the coefficient matrices depending on the initial pair, the terminal of the cost function involving the initial pair together with the nonlinear terms of the conditional expectation. The main contributions are: firstly,the maximum principle is derived by using variational methods, which forms a flow of forward and backward stochastic difference equations(FBSDE); secondly, in the case of the system state being one-dimensional, the equilibrium control is obtained by solving the FBSDE with feedback gain based on several nonsymmetric Riccati equations; finally, the necessary and sufficient solvability condition for the time-inconsistent LQ control problem is presented explicitly. The key techniques adopted are the maximum principle and the solution to the FBSDE developed in this paper.

关键词： time-inconsistency open-loop equilibrium control maximum principle FBSDE nonsymmetric Riccati equations

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