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Modeling and Computation of Transboundary Industrial Pollution with Emission Permits Trading by Stochastic Differential Game

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  • Shuhua Chang
  • Xinyu Wang
  • Zheng Wang

Abstract

Transboundary industrial pollution requires international actions to control its formation and effects. In this paper, we present a stochastic differential game to model the transboundary industrial pollution problems with emission permits trading. More generally, the process of emission permits price is assumed to be stochastic and to follow a geometric Brownian motion (GBM). We make use of stochastic optimal control theory to derive the system of Hamilton-Jacobi-Bellman (HJB) equations satisfied by the value functions for the cooperative and the noncooperative games, respectively, and then propose a so-called fitted finite volume method to solve it. The efficiency and the usefulness of this method are illustrated by the numerical experiments. The two regions’ cooperative and noncooperative optimal emission paths, which maximize the regions’ discounted streams of the net revenues, together with the value functions, are obtained. Additionally, we can also obtain the threshold conditions for the two regions to decide whether they cooperate or not in different cases. The effects of parameters in the established model on the results have been also examined. All the results demonstrate that the stochastic emission permits prices can motivate the players to make more flexible strategic decisions in the games.

Suggested Citation

  • Shuhua Chang & Xinyu Wang & Zheng Wang, 2015. "Modeling and Computation of Transboundary Industrial Pollution with Emission Permits Trading by Stochastic Differential Game," PLOS ONE, Public Library of Science, vol. 10(9), pages 1-29, September.
    • Handle: RePEc:plo:pone00:0138641
    DOI: 10.1371/journal.pone.0138641
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    References listed on IDEAS

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    Cited by:

    1. Wenguang Tang & Shuhua Zhang, 2019. "Modeling and Computation of Transboundary Pollution Game Based on Joint Implementation Mechanism," Complexity, Hindawi, vol. 2019, pages 1-18, August.
    2. Shuhua Chang & Suresh P. Sethi & Xinyu Wang, 2018. "Optimal Abatement and Emission Permit Trading Policies in a Dynamic Transboundary Pollution Game," Dynamic Games and Applications, Springer, vol. 8(3), pages 542-572, September.
    3. Chang, Shuhua & Wang, Xinyu & Wang, Zheng, 2016. "Modelling and computing the peaks of carbon emission with balanced growth," Chaos, Solitons & Fractals, Elsevier, vol. 91(C), pages 452-460.
    4. Kar, Saibal & Majumdar, Devleena, 2021. "Transboundary pollution, land use and abatement policy," Economic Analysis and Policy, Elsevier, vol. 72(C), pages 169-175.
    5. Wang, Xinyu & Zhang, Yuxing & Zhang, Shuhua, 2024. "Dynamic order allocation in a duopoly hybrid workforce of competition: A machine learning approach," European Journal of Operational Research, Elsevier, vol. 315(2), pages 668-690.
    6. Lai, Junyu & Wan, Justin W.L. & Zhang, Shuhua, 2019. "Numerical methods for two person games arising from transboundary pollution with emission permit trading," Applied Mathematics and Computation, Elsevier, vol. 350(C), pages 11-31.

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