A model of strategic sustainable investment

TL;DR

This paper models a continuous-time, infinite-horizon game between an investor and a firm focusing on optimal investment and emission reduction, providing explicit solutions and boundary-driven strategies.

Contribution

It introduces a new game-theoretic framework for joint investment and emission reduction, with explicit solutions in the zero-noise limit and a verification theorem for the system.

Findings

Optimal actions are triggered by moving boundaries increasing with emission abatement

Explicit solutions are constructed in the zero-noise limit

Numerical approximations illustrate boundary-driven strategies

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.