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Optimal Carbon Emission Control With Allowances Purchasing

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Listed:
  • Xinfu Chen
  • Yuchao Dong
  • Wenlin Huang
  • Jin Liang

Abstract

In this paper, we consider a company can simultaneously reduce its emissions and buy carbon allowances at any time. We establish an optimal control model involving two stochastic processes with two control variables, which is a singular control problem. This model can then be converted into a Hamilton-Jacobi-Bellman (HJB) equation, which is a two-dimensional variational equality with gradient barrier, so that the free boundary is a surface. We prove the existence and uniqueness of the solution. Finally, some numerical results are shown.

Suggested Citation

  • Xinfu Chen & Yuchao Dong & Wenlin Huang & Jin Liang, 2024. "Optimal Carbon Emission Control With Allowances Purchasing," Papers 2407.08477, arXiv.org.
    • Handle: RePEc:arx:papers:2407.08477
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    File URL: http://arxiv.org/pdf/2407.08477
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    References listed on IDEAS

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    2. Merton, Robert C., 1971. "Optimum consumption and portfolio rules in a continuous-time model," Journal of Economic Theory, Elsevier, vol. 3(4), pages 373-413, December.
    3. Jin Liang & Wenlin Huang, 2020. "Optimal Control Strategy of Companies: Inheriting Period and Carbon Emission Reduction," Mathematical Problems in Engineering, Hindawi, vol. 2020, pages 1-11, November.
    4. Merton, Robert C, 1969. "Lifetime Portfolio Selection under Uncertainty: The Continuous-Time Case," The Review of Economics and Statistics, MIT Press, vol. 51(3), pages 247-257, August.
    5. Matti Liski & Juan-Pablo Montero, 2005. "A Note on Market Power in an Emission Permits Market with Banking," Environmental & Resource Economics, Springer;European Association of Environmental and Resource Economists, vol. 31(2), pages 159-173, June.
    6. Rubin, Jonathan D., 1996. "A Model of Intertemporal Emission Trading, Banking, and Borrowing," Journal of Environmental Economics and Management, Elsevier, vol. 31(3), pages 269-286, November.
    7. Min Dai & Steven Kou & Shuaijie Qian & Xiangwei Wan, 2022. "Nonconcave Utility Maximization with Portfolio Bounds," Management Science, INFORMS, vol. 68(11), pages 8368-8385, November.
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