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

Paper: arXiv 2601.11348

Authors: 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.

Complexity vs Empirical Score

• Math Complexity: 8.5/10
• Empirical Rigor: 2.5/10
• Quadrant: Lab Rats — theoretically deep, empirically untested

Why this score: The paper provides a rigorous mathematical framework using stochastic control, Hamilton-Jacobi-Bellman (HJB) equations, and viscosity solutions to address carbon abatement with ratcheting constraints. However, it is purely theoretical with synthetic numerical illustrations and lacks empirical validation against real-world carbon emission datasets.

Research Flowchart

  flowchart TD
    A[Research Goal: Find optimal carbon abatement schedule under budget constraints] --> B[Inputs: Allocated carbon budget & stochastic budget update process]
    B --> C[Formulate Stochastic Control Problem with ratcheting constraint]
    C --> D[Derive Hamilton-Jacobi-Bellman HJB Equation]
    D --> E[Prove Value Function is unique Viscosity Solution & solve numerically]
    E --> F[Outcomes: Optimal non-increasing emission schedule & quantified constraint impact]