Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

Decarbonization of financial markets: a mean-field game approach

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.

Decarbonization of financial markets: a mean-field game approach

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.
Paper Structure (25 sections, 19 theorems, 160 equations, 5 figures, 2 tables, 1 algorithm)

This paper contains 25 sections, 19 theorems, 160 equations, 5 figures, 2 tables, 1 algorithm.

Table of Contents

  1. Introduction
  2. Related literature
  3. A mean-field game model of decarbonization
  4. The representative firm problem
  5. The investors problem
  6. Market equilibrium
  7. Mean-field game equilibrium of companies
  8. Market completeness
  9. Solution to the mean field game problem
  10. Additional notations
  11. Main results
  12. Proof of Theorem \ref{['main.thm']}
  13. Proof of Theorem \ref{['thm:convergence-result']}
  14. Examples and illustrations
  15. Detailed implementation of Algorithm \ref{['algorithm']}
  16. ...and 10 more sections

Key Result

Lemma 1

For any $\psi$ such that $\int_0^T \psi_s^2 ds <+\infty$ a.s., the equation eq:state-equation has a unique solution given by

Figures (5)

  • Figure 1: Structure of the game.
  • Figure 2: Convergence of the distribution of stochastic discount factor $\xi$ (left graph) and of the total average emissions.
  • Figure 3: Distribution of total average emissions (left) and expected emissions of the representative company per unit of time (right), for different values of the volatility of emission penalty $\gamma$.
  • Figure 4: Distribution of total average emissions (left) and expected emissions of the representative company per unit of time (right), for different values of the environmental concern of green investors $\lambda$.
  • Figure 5: Distribution of total average emissions (left) and expected emissions of the representative company per unit of time (right), for different values of the proportion of green investors $\rho$.

Theorems & Definitions (42)

  • Lemma 1
  • proof
  • Lemma 2
  • proof
  • Remark 1
  • Lemma 3
  • proof
  • Definition 1
  • Theorem 1
  • Theorem 2
  • ...and 32 more