Optimal Incentive for Regulated Production

Paper: arXiv 2506.14286

Authors: Benhao Du, Thomas Treillard, Francois Wang

Abstract

This paper explores stochastic control models in the context of decarbonization within the energy market. We study three progressively complex scenarios: (1) a single firm operating with two technologies-one polluting and one clean,(2)two firms model and (3) two firms without any regulatory incentive. For each setting, we formulate the corresponding stochastic control problem and characterize the firms’ optimal strategies in terms of investment and production. The analysis highlights the strategic interactions between firms and the role of incentives in accelerating the transition to cleaner technologies.

Complexity vs Empirical Score

• Math Complexity: 8.5/10
• Empirical Rigor: 1.5/10
• Quadrant: Lab Rats — theoretically deep, empirically untested

Why this score: The paper presents a rigorous theoretical framework using stochastic control, Hamilton-Jacobi-Bellman PDEs, and systems of non-linear ODEs to model decarbonization incentives. However, it lacks any empirical validation, real-world data application, or backtesting, relying solely on synthetic numerical illustrations.

Research Flowchart

  flowchart TD
    A[Research Goal: Optimal Incentives for Energy Decarbonization] --> B[Model Setup: 1-Firm & 2-Firm Settings]
    B --> C[Inputs: Polluting vs Clean Tech, Energy Prices, Subsidies]
    C --> D[Stochastic Control & Game Theory Formulation]
    D --> E[Derive Optimal Investment & Production Strategies]
    E --> F[Findings: Strategic Interactions & Dynamic Incentive Design]