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Optimal dynamic regulation of carbon emissions market

Author

Listed:
  • René Aïd
  • Sara Biagini
Abstract
In this article, we deal with optimal dynamic carbon emission regulation of a set of firms. On the one hand, the regulator dynamically allocates emission allowances to each firm. On the other hand, firms face idiosyncratic, as well as common, economic shocks on emissions, and they have linear quadratic abatement costs. Firms can trade allowances so as to minimize total expected costs, which arise from abatement, trading, and terminal penalty. Using variational methods, we first exhibit in closed form the market equilibrium in function of the regulator's dynamic allocation. We then solve the Stackelberg game between the regulator and the firms. The result is a closed‐form expression of the optimal dynamic allocation policies that allow a desired expected emission reduction. The optimal policy is unique in the presence of market impact. In absence of market impact, the optimal policy is nonunique, but all the optimal policies share common properties. The optimal policies are fully responsive, and therefore induce a constant abatement effort and a constant price of allowances. Our results are robust to some extensions, like different penalty functions.

Suggested Citation

  • René Aïd & Sara Biagini, 2023. "Optimal dynamic regulation of carbon emissions market," Mathematical Finance, Wiley Blackwell, vol. 33(1), pages 80-115, January.
    • Handle: RePEc:bla:mathfi:v:33:y:2023:i:1:p:80-115
    DOI: 10.1111/mafi.12364
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    References listed on IDEAS

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    Cited by:

    1. Barbara Annicchiarico & Marco Carli & Francesca Diluiso, 2022. "Climate Policies, Macroprudential Regulation, and the Welfare Cost of Business Cycles," CEIS Research Paper 543, Tor Vergata University, CEIS, revised 31 Oct 2022.
    2. Gianmarco Del Sarto & Marta Leocata & Giulia Livieri, 2024. "A Mean Field Game approach for pollution regulation of competitive firms," Papers 2407.12754, arXiv.org.

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