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Weak Closed-Loop Solvability of Stochastic Linear Quadratic Optimal Control Problems of Markovian Regime Switching System

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Abstract

In this paper, we investigate open-loop and weak closed-loop solvabilities of stochastic linear quadratic (LQ, for short) optimal control problem of Markovian regime switching system. Interestingly, these two solvabilities are equivalent on [0, T). We first provide an alternative characterization of the open-loop solvability of LQ problem using a perturbation approach. Then, we study the weak closed-loop solvability of LQ problem of Markovian regime switching system, and establish the equivalent relationship between open-loop and weak closed-loop solvabilities. Finally, we present an example to shed on light on finding weak closed-loop optimal strategies within the framework of Markovian regime switching system.

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Acknowledgements

The authors would like to thank the editors and the anonymous referees for many helpful comments and valuable suggestions on this paper.

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Authors and Affiliations

  1. Department of Mathematics, Southern University of Science and Technology, Shenzhen, 518055, Guangdong, China

    Jiaqiang Wen

  2. Department of Applied Mathematics, The Hong Kong Polytechnic University, Hong Kong, China

    Xun Li

  3. Department of Mathematics and SUSTech International center for Mathematics, Southern University of Science and Technology, Shenzhen, 518055, Guangdong, China

    Jie Xiong

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  1. Jiaqiang Wen
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  2. Xun Li
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  3. Jie Xiong
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Correspondence to Xun Li.

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Jiaqiang Wen was partially supported by National Natural Science Foundation of China (Grant Nos. 11871309, 11671229) and China Postdoctoral Science Foundation (Grant No. 2019M660968). Xun Li was partially supported by Research Grants Council of Hong Kong under Grants 15224215, 15255416 and 15213218. Jie Xiong was supported partially by Southern University of Science and Technology Start up fund Y01286120 and National Natural Science Foundation of China Grants 61873325 and 11831010.

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Wen, J., Li, X. & Xiong, J. Weak Closed-Loop Solvability of Stochastic Linear Quadratic Optimal Control Problems of Markovian Regime Switching System. Appl Math Optim 84, 535–565 (2021). https://doi.org/10.1007/s00245-020-09653-8

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