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Linear Quadratic Optimal Control Problems for Mean-Field Backward Stochastic Differential Equations

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Abstract

This paper is concerned with linear quadratic optimal control problems for mean-field backward stochastic differential equations (MF-BSDEs, for short) with deterministic coefficients. The optimality system, which is a linear mean-field forward–backward stochastic differential equation with constraint, is obtained by a variational method. By decoupling the optimality system, two coupled Riccati equations and an MF-BSDE are derived. It turns out that the coupled two Riccati equations are uniquely solvable. Then a complete and explicit representation is obtained for the optimal control.

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Acknowledgements

Xun Li was partially supported by Hong Kong RGC under Grants 15209614, 15224215 and 15255416. Jingrui Sun was partially supported by the National Natural Science Foundation of China (11401556) and the Fundamental Research Funds for the Central Universities (WK 2040000012). Jie Xiong acknowledges the financial support from FDCT 025/2016/A1. The authors would like to thank the anonymous referees for their suggestive comments, which lead to an improvement of the paper.

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Li, X., Sun, J. & Xiong, J. Linear Quadratic Optimal Control Problems for Mean-Field Backward Stochastic Differential Equations. Appl Math Optim 80, 223–250 (2019). https://doi.org/10.1007/s00245-017-9464-7

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