IDEAS home Printed from https://ideas.repec.org/a/eee/apmaco/v350y2019icp11-31.html
   My bibliography  Save this article

Numerical methods for two person games arising from transboundary pollution with emission permit trading

Author

Listed:
  • Lai, Junyu
  • Wan, Justin W.L.
  • Zhang, Shuhua

Abstract

We propose finite difference methods for solving two dimensional Hamilton–Jacobi–Bellman (HJB) equations and systems arising from the modelling of transboundary pollution with emission permits trading. We prove that our numerical scheme for the HJB equations from cooperative game is consistent, stable, and monotone, therefore guarantees convergence to viscosity solutions. To ensure our scheme is fully implicit and unconditionally monotone, we combine wide stencil with narrow stencil in the discretization. We address coupling between unknown variables and emission controls using policy iteration. We solve the coupled systems of HJB equations from non-cooperative game efficiently through policy-like iteration. We give a theoretical analysis of our scheme for solving the coupled system and find that it converges under certain conditions. Finally, we show that our numerical scheme achieves higher order of convergence than the finite volume method proposed originally.

Suggested Citation

  • 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.
  • Handle: RePEc:eee:apmaco:v:350:y:2019:i:c:p:11-31
    DOI: 10.1016/j.amc.2018.12.053
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0096300318311147
    Download Restriction: Full text for ScienceDirect subscribers only

    File URL: https://libkey.io/10.1016/j.amc.2018.12.053?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Swathi Amarala & Justin W. L. Wan, 2016. "Numerical methods for dynamic Bertrand oligopoly and American options under regime switching," Quantitative Finance, Taylor & Francis Journals, vol. 16(11), pages 1741-1762, November.
    2. 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.
    3. Seifert, Jan & Uhrig-Homburg, Marliese & Wagner, Michael, 2008. "Dynamic behavior of CO2 spot prices," Journal of Environmental Economics and Management, Elsevier, vol. 56(2), pages 180-194, September.
    4. Shoude Li, 2014. "A Differential Game of Transboundary Industrial Pollution with Emission Permits Trading," Journal of Optimization Theory and Applications, Springer, vol. 163(2), pages 642-659, November.
    5. Daskalakis, George & Psychoyios, Dimitris & Markellos, Raphael N., 2009. "Modeling CO2 emission allowance prices and derivatives: Evidence from the European trading scheme," Journal of Banking & Finance, Elsevier, vol. 33(7), pages 1230-1241, July.
    6. Copeland, Brian R & Taylor, M Scott, 1995. "Trade and Transboundary Pollution," American Economic Review, American Economic Association, vol. 85(4), pages 716-737, September.
    7. D. W. K. Yeung, 2007. "Dynamically Consistent Cooperative Solution in a Differential Game of Transboundary Industrial Pollution," Journal of Optimization Theory and Applications, Springer, vol. 134(1), pages 143-160, July.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Yunpeng Yang & Zhiqiang Liu & Hongmin Chen & Yaqiong Wang & Guanghui Yuan, 2020. "Evaluating Regional Eco-Green Cooperative Development Based on a Heterogeneous Multi-Criteria Decision-Making Model: Example of the Yangtze River Delta Region," Sustainability, MDPI, vol. 12(7), pages 1-20, April.
    2. Wenzhuo Sun & Zheng Liu, 2023. "Third-Party Governance of Groundwater Ammonia Nitrogen Pollution: An Evolutionary Game Analysis Considering Reward and Punishment Distribution Mechanism and Pollution Rights Trading Policy," Sustainability, MDPI, vol. 15(11), pages 1-16, June.
    3. Weixin Yang & Yunpeng Yang, 2020. "Research on Air Pollution Control in China: From the Perspective of Quadrilateral Evolutionary Games," Sustainability, MDPI, vol. 12(5), pages 1-23, February.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. 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.
    2. 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.
    3. Wang, Xinyu & Sethi, Suresh P. & Chang, Shuhua, 2022. "Pollution abatement using cap-and-trade in a dynamic supply chain and its coordination," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 158(C).
    4. Shuhua Chang & Xinyu Wang & Alexander Shananin, 2015. "Modeling and Computation of Mean Field Equilibria in Producers' Game with Emission Permits Trading," Papers 1506.04869, arXiv.org.
    5. Fang, Sheng & Lu, Xinsheng & Li, Jianfeng & Qu, Ling, 2018. "Multifractal detrended cross-correlation analysis of carbon emission allowance and stock returns," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 509(C), pages 551-566.
    6. Julien Chevallier & Benoît Sévi, 2014. "On the Stochastic Properties of Carbon Futures Prices," Environmental & Resource Economics, Springer;European Association of Environmental and Resource Economists, vol. 58(1), pages 127-153, May.
    7. Dahlen, Niklas & Fehrenkötter, Rieke & Schreiter, Maximilian, 2024. "The new bond on the block — Designing a carbon-linked bond for sustainable investment projects," The Quarterly Review of Economics and Finance, Elsevier, vol. 95(C), pages 316-325.
    8. Zheng, Zeyu & Xiao, Rui & Shi, Haibo & Li, Guihong & Zhou, Xiaofeng, 2015. "Statistical regularities of Carbon emission trading market: Evidence from European Union allowances," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 426(C), pages 9-15.
    9. Zhao, Xin-gang & Wu, Lei & Li, Ang, 2017. "Research on the efficiency of carbon trading market in China," Renewable and Sustainable Energy Reviews, Elsevier, vol. 79(C), pages 1-8.
    10. repec:ipg:wpaper:2014-082 is not listed on IDEAS
    11. Chang-Yi Li & Son-Nan Chen & Shih-Kuei Lin, 2016. "Pricing derivatives with modeling CO emission allowance using a regime-switching jump diffusion model: with regime-switching risk premium," The European Journal of Finance, Taylor & Francis Journals, vol. 22(10), pages 887-908, August.
    12. Shawkat Hammoudeh & Duc Khuong Nguyen & Ricardo M. Sousa, 2014. "What explains the short," Working Papers 2014-81, Department of Research, Ipag Business School.
    13. Julien Chevallier & Stéphane Goutte, 2014. "The goodness-of-fit of the fuel-switching price using the mean-reverting Lévy jump process," Working Papers 2014-285, Department of Research, Ipag Business School.
    14. Huang, Zhehao & Dong, Hao & Jia, Shuaishuai, 2022. "Equilibrium pricing for carbon emission in response to the target of carbon emission peaking," Energy Economics, Elsevier, vol. 112(C).
    15. Sharon S. Yang & Jr-Wei Huang & Chuang-Chang Chang, 2016. "Detecting and modelling the jump risk of CO 2 emission allowances and their impact on the valuation of option on futures contracts," Quantitative Finance, Taylor & Francis Journals, vol. 16(5), pages 749-762, May.
    16. Hammoudeh, Shawkat & Nguyen, Duc Khuong & Sousa, Ricardo M., 2014. "What explain the short-term dynamics of the prices of CO2 emissions?," Energy Economics, Elsevier, vol. 46(C), pages 122-135.
    17. Po Yun & Chen Zhang & Yaqi Wu & Yu Yang, 2022. "Forecasting Carbon Dioxide Price Using a Time-Varying High-Order Moment Hybrid Model of NAGARCHSK and Gated Recurrent Unit Network," IJERPH, MDPI, vol. 19(2), pages 1-19, January.
    18. Wugan Cai & Jiafeng Pan, 2017. "Stochastic Differential Equation Models for the Price of European CO 2 Emissions Allowances," Sustainability, MDPI, vol. 9(2), pages 1-12, February.
    19. Cong, Ren & Lo, Alex Y., 2017. "Emission trading and carbon market performance in Shenzhen, China," Applied Energy, Elsevier, vol. 193(C), pages 414-425.
    20. repec:hum:wpaper:sfb649dp2014-050 is not listed on IDEAS
    21. Hintermann, Beat & Peterson, Sonja & Rickels, Wilfried, 2014. "Price and market behavior in Phase II of the EU ETS," Kiel Working Papers 1962, Kiel Institute for the World Economy (IfW Kiel).
    22. Charles, Amélie & Darné, Olivier & Fouilloux, Jessica, 2011. "Testing the martingale difference hypothesis in CO2 emission allowances," Economic Modelling, Elsevier, vol. 28(1), pages 27-35.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:apmaco:v:350:y:2019:i:c:p:11-31. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: https://www.journals.elsevier.com/applied-mathematics-and-computation .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.