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The Optimal Control of Fully-Coupled Forward-Backward Doubly Stochastic Systems Driven by Itô-Lévy Processes

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Abstract

This paper studies the optimal control of a fully-coupled forward-backward doubly stochastic system driven by Itô-Lévy processes under partial information. The existence and uniqueness of the solution are obtained for a type of fully-coupled forward-backward doubly stochastic differential equations (FBDSDEs in short). As a necessary condition of the optimal control, the authors get the stochastic maximum principle with the control domain being convex and the control variable being contained in all coefficients. The proposed results are applied to solve the forward-backward doubly stochastic linear quadratic optimal control problem.

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Authors and Affiliations

  1. School of Control Science and Engineering, Shandong University, Jinan, 250061, China

    Wencan Wang

  2. School of Mathematics and Statistics, Central South University, Changsha, 410083, China

    Jinbiao Wu & Zaiming Liu

Authors
  1. Wencan Wang
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  2. Jinbiao Wu
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  3. Zaiming Liu
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Corresponding author

Correspondence to Jinbiao Wu.

Additional information

This research was supported by the Cultivation Program of Distinguished Young Scholars of Shandong University under Grant No. 2017JQ06, the National Natural Science Foundation of China under Grant Nos. 11671404, 11371374, 61821004, 61633015, the Provincial Natural Science Foundation of Hunan under Grant No. 2017JJ3405.

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Wang, W., Wu, J. & Liu, Z. The Optimal Control of Fully-Coupled Forward-Backward Doubly Stochastic Systems Driven by Itô-Lévy Processes. J Syst Sci Complex 32, 997–1018 (2019). https://doi.org/10.1007/s11424-018-7300-z

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  • DOI: https://doi.org/10.1007/s11424-018-7300-z

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