Optimal timing for green technology investment under climate risk in a jump-diffusion framework

Climate change poses significant challenges to the company as global warming has an adverse impact on output. It is an urge for companies to explore innovative solutions to mitigate climate risks. In this paper, we study the optimal timing for implementing green technology to reduce the impact of global warming by investigating dynamic stochastic models. Initially, the company has the option to purchase insurance policies to transfer climate risk at the cost of paying insurance premiums. As green technology advances, agricultural companies have the alternative option of investing in green technology to reduce the impact of climate risk. The investment in implementing green technology is also highly variable over time due to ongoing innovations in the field. To account for this uncertainty, we model the evolution of investment costs using a compound Poisson process. We aim to maximize the company's consumption by finding the optimal green technology investment timing. A viscosity solution approach verifies existence and uniqueness under non-linearities induced by the jump process. Numerical analysis illustrates how climate risk volatility, insurance costs, and technological leapfrogging (via Poisson jump intensity) alter the optimal policy.