Advertisement

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
Article

Abstract

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.

Keywords

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

Mathematics Subject Classification

49J20 65N30 

Notes

Acknowledgements

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

References

  1. 1.
    Benchekroun H, Chaudhuri A (2013) Transboundary pollution and clean technologies. Resour Energy Econ 36:601–619CrossRefGoogle Scholar
  2. 2.
    Bernard A, Haurie A, Vielle M, Viguier L (2008) A two-level dynamic game of carbon emission trading between Russia, China, and Annex B countries. J Econ Dyn Control 32:1830–1856MathSciNetCrossRefGoogle Scholar
  3. 3.
    Breton M, Zaccour G, Zahaf M (2005) A differential game of joint implementation of environmental projects. Automatica 41:1737–1749MathSciNetCrossRefGoogle Scholar
  4. 4.
    Chang K, Wang S, Peng K (2013) Mean reversion of stochastic convenience yields for CO\(_2\) emissions allowances: empirical evidence from the EU ETS. Span Rev Financ Econ 11:39–45CrossRefGoogle Scholar
  5. 5.
    Chang S, Wang X, Wang Z (2015) Modeling and computation of transboundary industrial pollution with emission permits trading by stochastic differential game. PLoS ONE 10:1–29Google Scholar
  6. 6.
    Chen Y, Lu Z (2015) High efficient and accuracy numerical methods for optimal control problems. Science Press, BeijingGoogle Scholar
  7. 7.
    Daskalakis G, Psychoyios D, Markellos R (2009) Modeling CO\(_2\) emission allowance prices and derivatives: evidence from the European trading scheme. J Bank Finance 33:1230–1241CrossRefGoogle Scholar
  8. 8.
    Falcone M (2006) Numerical methods for differential game based on partial differential equations. Int Game Theory Rev 8:231–272MathSciNetCrossRefGoogle Scholar
  9. 9.
    Feng Y, Li C, Huang T (2016) Sandwich control systems with impulse time windows. Int J Mach Learn Cyber.  https://doi.org/10.1007/s13042-016-0580-5 CrossRefGoogle Scholar
  10. 10.
    Feng Y, Li C, Huang T (2016) Periodically multiple state-jumps impulsive control systems with impulse time windows. Neurocomputing 193:7–13CrossRefGoogle Scholar
  11. 11.
    Feng Y, Yu J, Li C, Huang T, Che H (2017) Linear impulsive control system with impulse time windows. J Vib Control 23(1):111–118MathSciNetCrossRefGoogle Scholar
  12. 12.
    Feng Y, Tu D, Li C, Huang T (2015) Uniformly stability of impulsive delayed linear systems with impulse time windows. Ital J Pure Appl Math 34:213–220MathSciNetzbMATHGoogle Scholar
  13. 13.
    Feng Y, Peng Y, Zou L, Tu Z, Liu J (2017) A note on impulsive control of nonlinear systems with impulse time window. J Nonlinear Sci Appl 10:3087–3098MathSciNetCrossRefGoogle Scholar
  14. 14.
    Feng Y, Zou L, Tu Z (2017) Stability analysis for a class of nonlinear impulsive switched systems. J Nonlinear Sci Appl 10:4544–4551MathSciNetCrossRefGoogle Scholar
  15. 15.
    Feng Y, Lu Z, Cao L, Li L, Zhang S (2017) A priori error estimates of finite volume methods for general elliptic optimal control problems. Electr J Differ Equ 267:1–15MathSciNetzbMATHGoogle Scholar
  16. 16.
    Jensen M, Smears I (2013) On the convergence of finite element methods for Hamilton–Jacobi–Bellman equations. SIAM J Numer Anal 51:137–162MathSciNetCrossRefGoogle Scholar
  17. 17.
    Labriet M, Loulou R (2003) Coupling climate damages and GHG abatement costs in a linear programming framework. Environ Model Assess 8:261–274CrossRefGoogle Scholar
  18. 18.
    Leveque R (2004) Finite volume methods for hyperbolic problems. Cambridge University Press, CambridgeGoogle Scholar
  19. 19.
    Li S (2014) A differential game of transboundary industrial pollution with emission permits trading. J Optim Theory Appl 163:642–659MathSciNetCrossRefGoogle Scholar
  20. 20.
    Li C, Yu X, Liu Z, Huang T (2016) Asynchronous impulsive containment control in switched multi-agent systems. Inf Sci 370–371(20):667–679CrossRefGoogle Scholar
  21. 21.
    Li H, Liao X, Huang T, Zhu W, Liu Y (2015) Second-order globally nonlinear consensus in multi-agent networks with random directional link failure. IEEE Trans Neural Netw Learn Syst 26(3):565–575MathSciNetCrossRefGoogle Scholar
  22. 22.
    Li H, Liao X, Huang T, Zhu W (2015) Event-triggering sampling based leader-following consensus in second-order multi-agent systems. IEEE Trans Autom Control 60(7):1998–2003MathSciNetCrossRefGoogle Scholar
  23. 23.
    Li H, Liao X, Chen G, Dong Z, Hill DJ, Huang T (2015) Event-triggered asynchronous intermittent communication strategy for synchronization in complex networks. Neural Netw 66:1–10CrossRefGoogle Scholar
  24. 24.
    Li H, Chen G, Liao X, Huang T (2016) Quantized data-based leader-following consensus of general discrete-time multi-agent systems. IEEE Trans Circuits Syst II Express Briefs 63(4):401–405CrossRefGoogle Scholar
  25. 25.
    Liu J, Mu L, Ye X (2011) An adaptive discontinuous finite volume method for elliptic probles. J Comput Appl Math 235:5422–5431MathSciNetCrossRefGoogle Scholar
  26. 26.
    List J, Mason C (2001) Optimal institutional arrangements for transboundary pollutants in a second-best world: evidence from a differential game with asymmetric players. J Environ Econ Manag 42:277–296CrossRefGoogle Scholar
  27. 27.
    Wang S (2004) A novel fitted finite volume method for the Black–Scholes equation governing option pricing. IMA J Numer Anal 24:699–720MathSciNetCrossRefGoogle Scholar
  28. 28.
    Wang S, Gao F, Teo K (1998) An upwind finite-difference method for the approximation of viscosity solutions to Hamilton–Jacobi–Bellman equations. IMA J Math Control Inf 17:167–178MathSciNetCrossRefGoogle Scholar
  29. 29.
    Wang Z, Murks A, Du W, Rong Z, Perc M (2011) Coveting the neighbors fitness as a means to resolve social dilemmas. J Theor Biol 277:19–26MathSciNetCrossRefGoogle Scholar
  30. 30.
    Wang Z, Szolnoki A, Perc M (2013) Optimal interdependence between networks for the evolution of cooperation. Sci Rep 3:2470–2470CrossRefGoogle Scholar
  31. 31.
    Wen S, Zeng Z, Huang T, Meng Q (2015) Lag synchronization of switched neural networks via neural activation function and applications in image encryption. IEEE Trans Neural Netw Learn Syst 26(7):1493–1502MathSciNetCrossRefGoogle Scholar
  32. 32.
    Yang X, Cao J, Qiu J (2015) \(p\)th moment exponential stochastic synchronization of coupled memristor-based neural networks with mixed delays via delayed impulsive control. Neural Netw 65:80–91CrossRefGoogle Scholar
  33. 33.
    Yang X, Yang Z, Nie X (2014) Exponential synchronization of discontinuous chaotic systems via delayed impulsive control and its application to secure communication. Commun Nonlinear Sci Numer Simul 19:1529–1543MathSciNetCrossRefGoogle Scholar
  34. 34.
    Yeung D (2007) Dynamically consistent cooperative solution in a differential game of transboundary industrial pollution. J Optim Theory Appl 134:143–160MathSciNetCrossRefGoogle Scholar
  35. 35.
    Yeung D, Petrosyan L (2008) A cooperative stochastic differential game of transboundary industrial pollution. Automatica 44:1532–1544MathSciNetCrossRefGoogle Scholar

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

Personalised recommendations