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A maximum principle for optimal control problem of fully coupled forward-backward stochastic systems with partial information

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Abstract

The paper is concerned with a stochastic optimal control problem in which the controlled system is described by a fully coupled nonlinear forward-backward stochastic differential equation driven by a Brownian motion. It is required that all admissible control processes are adapted to a given subfiltration of the filtration generated by the underlying Brownian motion. For this type of partial information control, one sufficient (a verification theorem) and one necessary conditions of optimality are proved. The control domain need to be convex and the forward diffusion coefficient of the system can contain the control variable.

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Authors and Affiliations

  1. Department of Mathematical Sciences, Huzhou University, Zhejiang, 313000, China

    QingXin Meng

  2. Institute of Mathematics, Fudan University, Shanghai, 200433, China

    QingXin Meng

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  1. QingXin Meng
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Correspondence to QingXin Meng.

Additional information

This work was partially supported by Basic Research Program of China (Grant No. 2007CB814904), National Natural Science Foundation of China (Grant No. 10325101) and Natural Science Foundation of Zhejiang Province (Grant No. Y605478, Y606667)

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Meng, Q. A maximum principle for optimal control problem of fully coupled forward-backward stochastic systems with partial information. Sci. China Ser. A-Math. 52, 1579–1588 (2009). https://doi.org/10.1007/s11425-009-0114-7

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  • DOI: https://doi.org/10.1007/s11425-009-0114-7

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