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Delayed Stochastic Linear-Quadratic Control Problem and Related Applications

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  • Li Chen
  • Zhen Wu
  • Zhiyong Yu

Abstract

We discuss a quadratic criterion optimal control problem for stochastic linear system with delay in both state and control variables. This problem will lead to a kind of generalized forward-backward stochastic differential equations (FBSDEs) with Itô’s stochastic delay equations as forward equations and anticipated backward stochastic differential equations as backward equations. Especially, we present the optimal feedback regulator for the time delay system via a new type of Riccati equations and also apply to a population optimal control problem.

Suggested Citation

  • Li Chen & Zhen Wu & Zhiyong Yu, 2012. "Delayed Stochastic Linear-Quadratic Control Problem and Related Applications," Journal of Applied Mathematics, Hindawi, vol. 2012, pages 1-22, September.
    • Handle: RePEc:hin:jnljam:835319
    DOI: 10.1155/2012/835319
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    Cited by:

    1. René Carmona & Jean-Pierre Fouque & Seyyed Mostafa Mousavi & Li-Hsien Sun, 2018. "Systemic Risk and Stochastic Games with Delay," Journal of Optimization Theory and Applications, Springer, vol. 179(2), pages 366-399, November.
    2. Guatteri, Giuseppina & Masiero, Federica & Orrieri, Carlo, 2017. "Stochastic maximum principle for SPDEs with delay," Stochastic Processes and their Applications, Elsevier, vol. 127(7), pages 2396-2427.
    3. Jiequn Han & Ruimeng Hu, 2021. "Recurrent Neural Networks for Stochastic Control Problems with Delay," Papers 2101.01385, arXiv.org, revised Jun 2021.

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