Optimal timing of green technology adoption for climate risk mitigation

In this paper, we investigate the optimal timing for implementing green technology to mitigate the impact of rising temperatures on a company's consumption, where consumption is modeled as a jump-diffusion process to capture both continuous fluctuations and sudden changes. Rising temperatures negatively affect consumption, prompting the company to invest in green technology to counter these adverse effects. To account for variability in technological advancements, the evolution of technology costs is modeled by a compound Poisson process. Our objective is to determine the optimal investment threshold that maximizes the company's consumption under dynamic stochastic models related to climate change. The stopping problem is reformulated as a free-boundary problem, and by solving the associated Hamilton-Jacobi-Bellman (HJB) equation, a semi-closed-form solution for the optimal boundary is derived. We extend our optimal timing model for investments in green technology by incorporating insurance coverage and examine how the purchase of insurance affects the optimal investment threshold. We further provide numerical analysis to demonstrate the influence of various parameters on the optimal investment boundary, offering practical insights for decision-makers.