Two-stage optimal control models are a useful tool to model stochastic shocks, which have the potential to significantly alter the characteristics of a dynamic system, but cannot be controlled by the decision maker. Applications can be found in a wide range of topics including health and environmental economics.
The MODIBE model is a dynamic household model, in which households face stochastic environmental hazards, which can lead to a loss of their wealth. To respond to the risk, households can either relocate to a safer area or undertake preventive measures to protect their physical assets. Both actions require material and immaterial resources, which constrain the household's decision.