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Linear-quadratic optimal control for partially observed forward-backward stochastic systems with random jumps

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Abstract

In this paper, we investigate a linear-quadratic (LQ) optimal control problem for partially observed forward-backward stochastic systems with random jumps, where the observation’s drift term is linear with respect to the state x and control variable v. In our model, the observation process is no longer a Brownian motion but a controlled stochastic process driven by Brownian motions and Poisson random measures, which also have correlated noises with the state equation. Applying a backward separation approach to decompose the state and observation, we overcome the problem of cyclic dependence of control and observation. Then, the necessary and sufficient conditions for optimal control are derived. We also obtain the feedback representation of optimal control and provide two special cases to illustrate the significance of our results. Moreover, we also provide a financial application to demonstrate the practical significance of our results.

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Acknowledgements

This work was supported by National Natural Science Foundation of China (Grant Nos. 11831010, 61961160-732, 61821004, 61925306, 12001319), Shandong Provincial Natural Science Foundation (Grant Nos. ZR2019ZD42, ZR2020ZD24, ZR2020QA025), and Taishan Scholars Climbing Program of Shandong (Grant No. TSPD20210302).

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Authors and Affiliations

  1. Zhongtai Securities Institute for Financial Studies, Shandong University, Jinan, 250100, China

    Tian Chen

  2. School of Control Science and Engineering, Shandong University, Jinan, 250061, China

    Guangchen Wang

  3. School of Mathematics, Shandong University, Jinan, 250100, China

    Zhen Wu

Authors
  1. Tian Chen
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  2. Guangchen Wang
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  3. Zhen Wu
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Correspondence to Zhen Wu.

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Chen, T., Wang, G. & Wu, Z. Linear-quadratic optimal control for partially observed forward-backward stochastic systems with random jumps. Sci. China Inf. Sci. 65, 212205 (2022). https://doi.org/10.1007/s11432-021-3559-3

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  • DOI: https://doi.org/10.1007/s11432-021-3559-3

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