Natural disasters, mitigation investment and financial aid

We consider firms facing the risk of natural disasters and study their problem of investing in mitigation if financial insurance is not available. The firms' problem is to choose the optimal timing and size of the investment. The timing problem leads to a critical productivity size where firms above it invest in mitigation while firms below the threshold decide to not invest. We investigate how cash aid such as emergency response, and in-kind aid such as reconstruction, rehabilitation or disaster risk reduction investments, affect the critical productivity threshold and the optimal investment size and characterize the international donor's optimal charity strategy.