Abstract: As extreme weather events become more frequent and severe, firms face growing physical climate risk. Repeated shocks can cause persistent losses, weaken profitability, and eventually threaten continued operation. Firms must therefore decide how to address damage already incurred while limiting their exposure to future events. We develop a real-options model in which a firm’s revenue evolves continuously but is also subject to proportional losses from extreme events arriving at random times. The firm can undertake one irreversible investment: epair, which partially restores capacity lost to past events, or insurance, which reduces the severity of future losses. The firm can also abandon the market, either before or after investing. We characterize how these choices depend on current revenue and the number of events already experienced. After investment, each additional event raises the revenue threshold required to continue operating. Beyond a finite number of events, exit is optimal regardless of revenue. Before investment, the firm may wait between a lower abandonment threshold and an upper investment threshold. Although the full decision problem has no analytical solution, we solve the embedded post-investment abandonment option analytically. We then propose an adaptive least squares Monte Carlo method designed for this setting, where continuous revenue fluctuations interact with rare, discrete shocks. The method directs simulation effort toward states where investment or abandonment decisions are likely to change, improving policy estimation while limiting computational cost. We apply the framework to an oil and gas operator that uses offshore wind power to reduce carbon costs linked to the EU carbon allowance price. In this use case, lightning strikes can suddenly reduce turbine capacity. We find that greater exposure to lightning does not necessarily lead to earlier investment because it can also raise insurance costs and diminish the value of repair. Price uncertainty likewise affects the two investments differently. When strikes are frequent, greater uncertainty delays repair but accelerates insurance. When strikes are rare, their effect on investment timing can be non-monotonic. These findings illustrate how the timing and type of investment depend jointly on accumulated damage, future hazard exposure, and market uncertainty.