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Linear Quadratic Optimal Control Problems of Delayed Backward Stochastic Differential Equations

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Abstract

This paper is concerned with a linear quadratic optimal control problem of delayed backward stochastic differential equations. An explicit representation is derived for the optimal control, which is a linear feedback of the entire past history and the expected value of the future state trajectory in a short period of time. To obtain the optimal feedback, a new class of delayed Riccati equations and delayed-advanced forward-backward stochastic differential equations are introduced. Furthermore, the unique solvability of their solutions are discussed in detail.

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Acknowledgements

The authors would like to thank the editor and two anonymous referees for their constructive and insightful comments for improving the quality of this work. Many thanks for discussion and suggestions with Professor Li Chen at China University of Mining and Technology (Beijing).

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  1. School of Mathematics, Shandong University, Jinan, 250100, People’s Republic of China

    Weijun Meng & Jingtao Shi

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  1. Weijun Meng
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  2. Jingtao Shi
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Correspondence to Jingtao Shi.

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This work is financially supported by the National Key R&D Program of China (2018YFB1305400), the National Natural Science Foundations of China (11971266, 11571205, 11831010), and Shandong Provincial Natural Science Foundations (Grant Nos. ZR2020ZD24, ZR2019ZD42).

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Meng, W., Shi, J. Linear Quadratic Optimal Control Problems of Delayed Backward Stochastic Differential Equations. Appl Math Optim 84 (Suppl 1), 523–559 (2021). https://doi.org/10.1007/s00245-021-09778-4

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