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Optimal Abatement Schedules for Excess Carbon Emissions Towards a Net-Zero Target

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  • Hansjoerg Albrecher
  • Nora Muler

Abstract

Achieving net-zero carbon emissions requires a transformation of energy systems, industrial processes, and consumption patterns. In particular, a transition towards that goal involves a gradual reduction of excess carbon emissions that are not essential for the well-functioning of society. In this paper we study this problem from a stochastic control perspective to identify the optimal gradual reduction of the emission rate, when an allocated excess carbon budget is used up over time. Assuming that updates of the available carbon budget follow a diffusion process, we identify the emission strategy that maximizes expected discounted emissions under the constraint of a non-increasing emission rate, with an additional term rewarding the amount of time for which the budget is not yet depleted. We establish a link of this topic to optimal dividend problems in insurance risk theory under ratcheting constraints and show that the value function is the unique viscosity solution of the associated Hamilton-Jacobi-Bellman equation. We provide numerical illustrations of the resulting optimal abatement schedule of emissions and a quantitative evaluation of the effect of the non-increasing rate constraint on the value function.

Suggested Citation

  • Hansjoerg Albrecher & Nora Muler, 2026. "Optimal Abatement Schedules for Excess Carbon Emissions Towards a Net-Zero Target," Papers 2601.11348, arXiv.org.
    • Handle: RePEc:arx:papers:2601.11348
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    References listed on IDEAS

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    1. Romuald Elie & Nizar Touzi, 2008. "Optimal lifetime consumption and investment under a drawdown constraint," Finance and Stochastics, Springer, vol. 12(3), pages 299-330, July.
    2. Hansjörg Albrecher & Pablo Azcue & Nora Muler, 2023. "Optimal dividends under a drawdown constraint and a curious square-root rule," Finance and Stochastics, Springer, vol. 27(2), pages 341-400, April.
    3. Borissov, Kirill & Bretschger, Lucas, 2022. "Optimal carbon policies in a dynamic heterogeneous world," European Economic Review, Elsevier, vol. 148(C).
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    5. Chonghu Guan & Zuo Quan Xu, 2023. "Optimal ratcheting of dividend payout under Brownian motion surplus," Papers 2308.15048, arXiv.org, revised Jul 2024.
    6. Bahman Angoshtari & Erhan Bayraktar & Virginia R. Young, 2018. "Optimal Dividend Distribution Under Drawdown and Ratcheting Constraints on Dividend Rates," Papers 1806.07499, arXiv.org, revised Mar 2019.
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    8. Hansjorg Albrecher & Jinxia Zhu, 2025. "On effects of present-bias on carbon emission patterns towards a net zero target," Papers 2510.27384, arXiv.org.
    9. Thonhauser, Stefan & Albrecher, Hansjorg, 2007. "Dividend maximization under consideration of the time value of ruin," Insurance: Mathematics and Economics, Elsevier, vol. 41(1), pages 163-184, July.
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