Neural Processing Letters

, Volume 48, Issue 2, pp 1089–1104 | Cite as

An Empirical Study for Transboundary Pollution of Three Gorges Reservoir Area with Emission Permits Trading

  • Zuliang Lu
  • Yuming FengEmail author
  • Shuhua Zhang
  • Lin Li
  • Longzhou Cao


In this paper, we discuss a cooperative stochastic differential game for the transboundary industrial pollution problems of Three Gorges Reservoir Area. Base on the stochastic optimal control theory, we derive the Hamilton–Jacobi–Bellman equations for the cooperative games. Furthermore we solve the Hamilton–Jacobi–Bellman equations by using a fitted finite volume method. Finally, an empirical study base on the datum of Three Gorges Reservoir Area is given to demonstrate the efficiency and usefulness of the numerical method.


Transboundary pollution Three Gorges Reservoir Area Fitted finite volume method Stochastic differential game Hamilton–Jacobi–Bellman equation 

Mathematics Subject Classification

49J20 65N30 



The authors express their thanks to the referees for their helpful suggestions, which lead to improvements of the presentation.


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Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2017

Authors and Affiliations

  • Zuliang Lu
    • 1
    • 2
  • Yuming Feng
    • 3
    • 4
    Email author
  • Shuhua Zhang
    • 2
  • Lin Li
    • 1
  • Longzhou Cao
    • 1
  1. 1.Key Laboratory for Nonlinear Science and System StructureChongqing Three Gorges UniversityChongqingPeople’s Republic of China
  2. 2.Research Center for Mathematics and EconomicsTianjin University of Finance and EconomicsTianjinPeople’s Republic of China
  3. 3.Key Laboratory of Intelligent Information Processing and Control of Chongqing Municipal Institutions of Higher EducationChongqing Three Gorges UniversityWanzhou, ChongqingPeople’s Republic of China
  4. 4.Chongqing Engineering Research Center of Internet of Things and Intelligent Control TechnologyChongqing Three Gorges UniversityWanzhou, ChongqingPeople’s Republic of China

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