On effects of present-bias on carbon emission patterns towards a net zero target

Paper: arXiv 2510.27384

Authors: Hansjörg Albrecher, Jinxia Zhu

Abstract

This paper explores the optimal policy for using an allocated carbon emission budget over time with the objective to maximize profit, by explicitly taking into account present-biased preferences of decision-makers, accounting for time-inconsistent preferences. The setup can be adapted to be applicable for either a (present-biased) individual or also for a company which seeks a balance between production and emission schedules. In particular, we use and extend stochastic control techniques developed for optimal dividend strategies in insurance risk theory for the present purpose. The approach enables a quantitative analysis to assess the effects of present-bias, of sustainability awareness, and the efficiency of a potential carbon tax in a simplified model. In some numerical implementations, we illustrate in what way a higher degree of present-bias leads to excess emission patterns, while placing greater emphasis on sustainability reduces carbon emissions. Furthermore, we show that for low levels of carbon tax, its increase has a positive effect on curbing emissions, while beyond a certain threshold that marginal impact gets considerably weaker.

Complexity vs Empirical Score

• Math Complexity: 8.0/10
• Empirical Rigor: 2.5/10
• Quadrant: Lab Rats — theoretically deep, empirically untested

Why this score: The paper provides a rigorous mathematical framework applying continuous-time stochastic control and intra-personal subgame equilibria (quasi-hyperbolic discounting) to carbon emission budgets. However, it lacks empirical validation or historical data backtesting, relying primarily on theoretical models and stylized numerical implementations.

Research Flowchart

  flowchart TD
    A[Research Goal: Model effects of present-bias on optimal carbon budget allocation] --> B[Model Inputs: Carbon budget, profit functions, present-bias factor, carbon tax]
    B --> C[Methodology: Stochastic Control & Time-Inconsistent Preference Theory]
    C --> D[Computational Implementation: Numerical analysis of emission schedules]
    D --> E1[Outcome 1: Higher present-bias accelerates budget depletion & excess emissions]
    D --> E2[Outcome 2: Higher sustainability awareness successfully curbs emissions]
    D --> E3[Outcome 3: Carbon tax effective up to a threshold; marginal impact decays]