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A Mean-Field Optimal Control for Fully Coupled Forward-Backward Stochastic Control Systems with Lévy Processes

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Abstract

This paper is concerned with a class of mean-field type stochastic optimal control systems, which are governed by fully coupled mean-field forward-backward stochastic differential equations with Teugels martingales associated to Lévy processes. In these systems, the coefficients contain not only the state processes but also their marginal distribution, and the cost function is of mean-field type as well. The necessary and sufficient conditions for such optimal problems are obtained. Furthermore, the applications to the linear quadratic stochastic optimization control problem are investigated.

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Authors and Affiliations

  1. College of Mathematics and Systems Science, Shandong University of Science and Technology, Qingdao, 266590, China

    Zhen Huang, Ying Wang & Xiangrong Wang

Authors
  1. Zhen Huang
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  2. Ying Wang
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  3. Xiangrong Wang
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Corresponding author

Correspondence to Ying Wang.

Additional information

This research was supported by the Major Basic Research Program of Natural Science Foundation of Shandong Province under Grant No. 2019A01 and the Natural Science Foundation of Shandong Province of China under Grant No. ZR2020MF062.

This paper was recommended for publication by Editor LIU Shujun.

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Huang, Z., Wang, Y. & Wang, X. A Mean-Field Optimal Control for Fully Coupled Forward-Backward Stochastic Control Systems with Lévy Processes. J Syst Sci Complex 35, 205–220 (2022). https://doi.org/10.1007/s11424-021-0077-5

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  • DOI: https://doi.org/10.1007/s11424-021-0077-5

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