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The Stochastic Maximum Principle for a Jump-Diffusion Mean-Field Model Involving Impulse Controls and Applications in Finance

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Abstract

This paper establishes a stochastic maximum principle for a stochastic control of mean-field model which is governed by a Lévy process involving continuous and impulse control. The authors also show the existence and uniqueness of the solution to a jump-diffusion mean-field stochastic differential equation involving impulse control. As for its application, a mean-variance portfolio selection problem has been solved.

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Acknowledgements

The authors would like to thank the Editor and the anonymous referees for their constructive and insightful comments for improving the quality of this work, and Prof. Yang Shen at York University, for many helpful discussions and suggestions.

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Authors and Affiliations

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

    Cailing Li, Zaiming Liu & Jinbiao Wu

  2. Research and Development Center, Agricultural Bank of China, Beijing, 100161, China

    Xiang Huang

Authors
  1. Cailing Li
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  2. Zaiming Liu
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  3. Jinbiao Wu
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  4. Xiang Huang
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Corresponding author

Correspondence to Jinbiao Wu.

Additional information

This paper was supported by the National Science Foundation of China under Grant No. 11671404 and the Fundamental Research Funds for the Central Universities of Central South University under Grant No. 10553320171635.

This paper was recommended for publication by Editor LIU Yungang.

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Li, C., Liu, Z., Wu, J. et al. The Stochastic Maximum Principle for a Jump-Diffusion Mean-Field Model Involving Impulse Controls and Applications in Finance. J Syst Sci Complex 33, 26–42 (2020). https://doi.org/10.1007/s11424-018-8095-7

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  • DOI: https://doi.org/10.1007/s11424-018-8095-7

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