Paper: arXiv 2301.09163

Authors: Pierre Lavigne, Peter Tankov

Abstract

We develop a financial market model in which a large population of firms chooses dynamic emission strategies under climate transition risk, interacting with both environmentally concerned and neutral investors. Firms face a trade-off between financial returns and environmental performance, while their decisions are coupled through an equilibrium stochastic discount factor determined by investors’ portfolio allocations. The framework is formulated as a mean-field game, for which we establish existence and uniqueness of a Nash equilibrium among firms. We propose a convergent numerical scheme to compute the equilibrium and use it to study how climate transition risk and green-minded investors affect decarbonization dynamics and asset prices. Our results show that uncertainty about future climate risks and policies increases aggregate emissions and widens valuation spreads between green and brown firms. Although environmentally concerned investors can partially offset these effects by raising the cost of capital for high-emission firms and incentivizing emission reductions, policy uncertainty weakens their impact. Even a large share of green-minded investors is insufficient to reverse emission growth when future climate policies are unclear, highlighting the crucial role of credible and predictable climate policy in enabling financial markets to support decarbonization.

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 provides a highly sophisticated mathematical model using mean-field games to analyze climate transition risk and asset pricing. However, it is primarily theoretical and numerical, lacking empirical backtesting or real-world financial dataset validation.

Research Flowchart

  flowchart TD
    A[Research Goal: Model firm decarbonization under climate risk & green investor influence] --> B[Framework: Mean-Field Game with Stochastic Discount Factor]
    B --> C[Inputs: Climate policy uncertainty & investor preferences green vs. neutral]
    C --> D[Computational Method: Convergent numerical scheme for Nash equilibrium]
    D --> E[Finding 1: High policy uncertainty increases emissions & widens green-brown valuation spreads]
    D --> F[Finding 2: Green investors lower emissions by raising capital costs for brown firms]
    E & F --> G[Outcome: Credible climate policy is essential; investor preference alone cannot drive decarbonization]