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Decentralized control of forward and backward stochastic difference system with nested asymmetric information

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  • Zhang, Shen
  • Xu, Juanjuan
  • Zhang, Huanshui

Abstract

This paper is concerned with the linear quadratic decentralized control of forward and backward stochastic difference system (FBSDS) with multiplicative noises and nested asymmetric information. The main contribution is to give the equivalent condition for the solvability of the problem and the explicit decentralized optimal controllers in terms of Riccati equations. The key technology is solving the forward and backward stochastic difference equations with partial information derived from stochastic maximum principle.

Suggested Citation

  • Zhang, Shen & Xu, Juanjuan & Zhang, Huanshui, 2024. "Decentralized control of forward and backward stochastic difference system with nested asymmetric information," Applied Mathematics and Computation, Elsevier, vol. 478(C).
    • Handle: RePEc:eee:apmaco:v:478:y:2024:i:c:s0096300324002959
    DOI: 10.1016/j.amc.2024.128834
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    References listed on IDEAS

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    1. Shen Zhang & Juanjuan Xu & Guangchen Wang & Huanshui Zhang, 2022. "LQ control of forward and backward stochastic difference system," International Journal of Systems Science, Taylor & Francis Journals, vol. 53(7), pages 1401-1415, May.
    2. Bouchard, Bruno & Touzi, Nizar, 2004. "Discrete-time approximation and Monte-Carlo simulation of backward stochastic differential equations," Stochastic Processes and their Applications, Elsevier, vol. 111(2), pages 175-206, June.
    3. Wu, Zhen & Zhuang, Yi, 2018. "Linear-quadratic partially observed forward–backward stochastic differential games and its application in finance," Applied Mathematics and Computation, Elsevier, vol. 321(C), pages 577-592.
    4. Liu, Jingmei & Liang, Xiao & Xu, Juanjuan, 2021. "Solution to the forward and backward stochastic difference equations with asymmetric information and application," Applied Mathematics and Computation, Elsevier, vol. 390(C).
    5. Guangchen Wang & Hua Xiao, 2015. "Arrow Sufficient Conditions for Optimality of Fully Coupled Forward–Backward Stochastic Differential Equations with Applications to Finance," Journal of Optimization Theory and Applications, Springer, vol. 165(2), pages 639-656, May.
    6. Qi, Qingyuan & Qiu, Zhenghong & Wang, Xianghua & Ji, Zhijian, 2022. "Asymmetric information control for stochastic systems with different intermittent observations," Applied Mathematics and Computation, Elsevier, vol. 412(C).
    7. Rudolf Kerschbamer & Nina Maderner, 2001. "Optimal Control of Upstream Pollution under Asymmetric Information," Environmental & Resource Economics, Springer;European Association of Environmental and Resource Economists, vol. 19(4), pages 343-360, August.
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