This thesis develops mathematical models to analyze environmental policies under uncertainties, focusing on carbon capture and storage (CCS) and Net-Zero strategies. The first model introduces a continuous-time optimal stopping and control framework, integrating CCS into decision-making process. Using neural networks to approximate the value function and the Fischer- Burmeister function to handle non-linearities, the model captures complex behavior and boundary conditions. The results show that emissions capture slows pollutant accumulation and delays optimal policy adoption, emphasizing trade-offs between immediate action and long-term impacts. The second model extends the analysis to NetZero policies, modeling the stochastic dynamics of pollution and emissions. A linear-quadratic optimal control problem leads to a system of ordinary differential equations (ODEs) that characterize optimal control policies, incorporating long-term pollution costs through terminal conditions. The findings highlight the interplay between emissions, costs, and uncertainties, providing insights into sustainable policy design. This thesis advances the understanding of environmental policy timing and control, offering tools to balance economic and environmental trade-offs and guide sustainable decision-making.