Abstract
In this paper, we investigate a kind of partial information linear-quadratic optimal control problem driven by a backward stochastic differential equation, where the state equation and the cost functional contain diffusion terms. Using maximum principle, we derive the corresponding Hamiltonian system, which is a conditional mean-field forward-backward stochastic differential equation. By the backward separation approach and the filtering technique, we get two Riccati equations, and a backward and a forward optimal filtering equations. Then a feedback form of optimal control is obtained. We also extend the control problem to the case of mean-field backward stochastic differential equation under partial information. A corresponding feedback form of optimal control is also obtained.
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Acknowledgements
This work was supported in part by National Natural Science Foundation of China (Grant Nos. 11371228, 61821004, 61633015). The authors would like to thank the anonymous referees for their valuable comments, which led to a much better version of this paper.
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Huang, P., Wang, G. & Zhang, H. A partial information linear-quadratic optimal control problem of backward stochastic differential equation with its applications. Sci. China Inf. Sci. 63, 192204 (2020). https://doi.org/10.1007/s11432-019-1473-3
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DOI: https://doi.org/10.1007/s11432-019-1473-3