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

  • Cailing Li
  • Zaiming Liu
  • Jinbiao Wu
  • Xiang Huang


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.


Impulse control jump-diffusion Markowitz’s mean-variance model stochastic maximum principle 


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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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Copyright information

© Institute of Systems Science, Academy of Mathematics and Systems Science, Chinese Academy of Sciences and Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  • Cailing Li
    • 1
  • Zaiming Liu
    • 1
  • Jinbiao Wu
    • 1
  • Xiang Huang
    • 2
  1. 1.School of Mathematics and StatisticsCentral South UniversityChangshaChina
  2. 2.Research and Development CenterAgricultural Bank of ChinaBeijingChina

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