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Time-Inconsistent Stochastic LQ Problem with Regime Switching

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Abstract

This paper investigates a time-inconsistent stochastic linear-quadratic problem with regime switching that is characterized via a finite-state Markov chain. Open-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.

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Author information

Authors and Affiliations

  1. College of Artificial Intelligence, Nankai University, Tianjin, 300350, China

    Binbin Si & Yuan-Hua Ni

  2. Key Laboratory of Intelligent Robotics of Tianjin, Tianjin, 300350, China

    Binbin Si & Yuan-Hua Ni

  3. Key Laboratory of Systems and Control, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing, 100190, China

    Ji-Feng Zhang

  4. School of Mathematical Sciences, University of Chinese Academy of Sciences, Beijing, 100049, China

    Ji-Feng Zhang

Authors
  1. Binbin Si
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  2. Yuan-Hua Ni
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  3. Ji-Feng Zhang
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Corresponding author

Correspondence to Yuan-Hua Ni.

Additional information

This research was supported in part by the National Key R&D Program of China under Grant No. 2018YFA0703800, and by the National Natural Science Foundation of China under Grant Nos. 61773222, 61877057 and 61973172.

This paper was recommended for publication by Editor LIU Yungang.

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Si, B., Ni, YH. & Zhang, JF. Time-Inconsistent Stochastic LQ Problem with Regime Switching. J Syst Sci Complex 33, 1733–1754 (2020). https://doi.org/10.1007/s11424-020-9017-z

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  • DOI: https://doi.org/10.1007/s11424-020-9017-z

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