
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. MSC2020 Classification : 93E20, 91A15, 49N90, 65K15
FOS: Economics and business, climate finance; HJB equations; impact investing; Nash equilibria; stochastic games, Mathematical Finance, Optimization and Control (math.OC), Optimization and Control, FOS: Mathematics, 93E20, 91A15, 49N90, 65K15, Mathematical Finance (q-fin.MF)
FOS: Economics and business, climate finance; HJB equations; impact investing; Nash equilibria; stochastic games, Mathematical Finance, Optimization and Control (math.OC), Optimization and Control, FOS: Mathematics, 93E20, 91A15, 49N90, 65K15, Mathematical Finance (q-fin.MF)
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