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Stochastic maximum principle for optimal control problems of forward-backward delay systems involving impulse controls

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Abstract

This paper is concerned with the optimal control problems of forward-backward delay systems involving impulse controls. The authors establish a stochastic maximum principle for this kind of systems. The most distinguishing features of the proposed problem are that the control variables consist of regular and impulsive controls, both with time delay, and that the domain of regular control is not necessarily convex. The authors obtain the necessary and sufficient conditions for optimal controls, which have potential applications in mathematical finance.

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Authors and Affiliations

  1. School of Mathematics, Shandong University, Jinan, 250100, China

    Shujun Wang & Zhen Wu

Authors
  1. Shujun Wang
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  2. Zhen Wu
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Corresponding author

Correspondence to Zhen Wu.

Additional information

This paper was supported by the Natural Science Foundation of China under Grant No. 61573217, 111 Project (B12023), the National High-Level Personnel of Special Support Program and the Chang Jiang Scholar Program of Chinese Education Ministry.

This paper was recommended for publication by Editor LIU Yungang.

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Wang, S., Wu, Z. Stochastic maximum principle for optimal control problems of forward-backward delay systems involving impulse controls. J Syst Sci Complex 30, 280–306 (2017). https://doi.org/10.1007/s11424-016-5039-y

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  • DOI: https://doi.org/10.1007/s11424-016-5039-y

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