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Fully Coupled Forward-Backward Stochastic Functional Differential Equations and Applications to Quadratic Optimal Control

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Abstract

This paper considers the fully coupled forward-backward stochastic functional differential equations (FBSFDEs) with stochastic functional differential equations as the forward equations and the generalized anticipated backward stochastic differential equations as the backward equations. The authors will prove the existence and uniqueness theorem for FBSFDEs. As an application, we deal with a quadratic optimal control problem for functional stochastic systems, and get the explicit form of the optimal control by virtue of FBSFDEs.

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Authors and Affiliations

  1. Institute of Finance and Statistics, School of Mathematical Sciences, Nanjing Normal University, Nanjing, 210023, China

    Xiaoming Xu

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  1. Xiaoming Xu
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Correspondence to Xiaoming Xu.

Additional information

This research was supported by the Program of Natural Science Research of Jiangsu Higher Education Institutions of China under Grant No. 17KJB110009.

This paper was recommended for publication by Editor LIU Yungang.

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Xu, X. Fully Coupled Forward-Backward Stochastic Functional Differential Equations and Applications to Quadratic Optimal Control. J Syst Sci Complex 33, 1886–1902 (2020). https://doi.org/10.1007/s11424-020-9027-x

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  • DOI: https://doi.org/10.1007/s11424-020-9027-x

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