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Turnpike Properties for Stochastic Linear-Quadratic Optimal Control Problems

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An Erratum to this article was published on 18 January 2023

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Abstract

This paper analyzes the limiting behavior of stochastic linear-quadratic optimal control problems in finite time-horizon [0, T] as T → ∞. The so-called turnpike properties are established for such problems, under stabilizability condition which is weaker than the controllability, normally imposed in the similar problem for ordinary differential systems. In dealing with the turnpike problem, a crucial issue is to determine the corresponding static optimization problem. Intuitively mimicking the deterministic situations, it seems to be natural to include both the drift and the diffusion expressions of the state equation to be zero as constraints in the static optimization problem. However, this would lead us to a wrong direction. It is found that the correct static problem should contain the diffusion as a part of the objective function, which reveals a deep feature of the stochastic turnpike problem.

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Acknowledgements

The authors would like to thank the associate editor and the anonymous referees for their suggestive comments, which lead to this improved version of the paper.

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Authors and Affiliations

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

    Jingrui Sun

  2. College of Mathematics and Statistics, Shenzhen University, Shenzhen, 518060, China

    Hanxiao Wang

  3. Department of Mathematics, University of Central Florida, Orlando, FL, 32816, USA

    Jiongmin Yong

Authors
  1. Jingrui Sun
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  2. Hanxiao Wang
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  3. Jiongmin Yong
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Correspondence to Hanxiao Wang.

Additional information

This work was supported by the National Natural Science Foundation of China (No. 11901280, 12271242, 12201424), Guangdong Basic and Applied Basic Research Foundation (No. 2021A1515010031), Shenzhen Fundamental Research General Program (No. JCYJ20220530112814032) and NSF (No. DMS-1812921).

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Sun, J., Wang, H. & Yong, J. Turnpike Properties for Stochastic Linear-Quadratic Optimal Control Problems. Chin. Ann. Math. Ser. B 43, 999–1022 (2022). https://doi.org/10.1007/s11401-022-0374-x

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  • DOI: https://doi.org/10.1007/s11401-022-0374-x

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