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Stochastic carbon regulation in continuous time

Author

Listed:
  • René Aïd

    (LEDa - Laboratoire d'Economie de Dauphine - IRD - Institut de Recherche pour le Développement - Université Paris Dauphine-PSL - PSL - Université Paris Sciences et Lettres - CNRS - Centre National de la Recherche Scientifique)

  • Sara Biagini

Abstract

We deal with optimal dynamic carbon emission regulation of a set of firms. While the results are essentially taken from Aïd and Biagini (2023), the focus here is more on the methodology and its framing in the applied mathematics literature. 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. They may also receive free allowances from the regulator to aid in compliance. Using variational methods, we first exhibit in closed-form the market equilibrium as function of the regulator's 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. In the presence of market frictions, optimal expected allocations are unique and the optimal allowances price is constant as well as abatement efforts and trading rates.

Suggested Citation

  • René Aïd & Sara Biagini, 2025. "Stochastic carbon regulation in continuous time," Post-Print hal-05492333, HAL.
    • Handle: RePEc:hal:journl:hal-05492333
    DOI: 10.1201/9781032636252-17
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