Paper: arXiv 2412.00986

Authors: Tiziano De Angelis, Caio César Graciani Rodrigues, Peter Tankov

Abstract

We study a problem of optimal irreversible investment and emission reduction formulated as a nonzero-sum dynamic game between an investor with environmental preferences and a firm. The game is set in continuous time on an infinite-time horizon. The firm generates profits with a stochastic dynamics and may spend part of its revenues towards emission reduction (e.g., renovating the infrastructure). The firm’s objective is to maximize the discounted expectation of a function of its profits. The investor participates in the profits, may decide to invest to support the firm’s production capacity and uses a profit function which accounts for both financial and environmental factors. Nash equilibria of the game are obtained via a system of variational inequalities. We formulate a general verification theorem for this system in a diffusive setup and construct an explicit solution in the zero-noise limit. Our explicit results and numerical approximations show that both the investor’s and the firm’s optimal actions are triggered by moving boundaries that increase with the total amount of emission abatement.

Complexity vs Empirical Score

  • Math Complexity: 8.5/10
  • Empirical Rigor: 3.0/10
  • Quadrant: Lab Rats — theoretically deep, empirically untested

Why this score: The paper presents a sophisticated theoretical continuous-time stochastic game using Hamilton-Jacobi-Bellman equations and verification theorems for sustainable investing. While highly novel and mathematically rigorous in its theoretical formulation, it relies primarily on numerical algorithms rather than empirical backtesting against real-world market datasets.

Research Flowchart

  flowchart TD
    A[Research Goal: Model Strategic ESG Investment <br>as a Nonzero-Sum Dynamic Game] --> B[Inputs: Stochastic Firm Profits, ESG Preferences,<br> Production & Abatement Parameters]
    B --> C[Formulate Infinite-Horizon Game <br>& System of Variational Inequalities]
    C --> D[Prove General Verification Theorem <br>in Diffusive Setup]
    D --> E[Compute Explicit Zero-Noise Solutions <br>& Numerical Approximations]
    E --> F[Key Outcome: Optimal Actions Triggered by <br>Moving Boundaries Increasing with Abatement]

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1 of 52 cited works are in the corpus; resolved via arXiv source bundles, Semantic Scholar and OpenAlex. Corpus-wide: 2518 linked papers.