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.

Flow Chart for household dynamics © Michael Freiberger

The underlying Hamilton-Jacobi-Bellman problem contains the unknown value-function of households V.

MODIBE Bellman formulation © Michael Freiberger

As solving for the the value-function analytically is impossible, the problem is solved numerically using a value-function iteration approach. A combination of several different optimisation techniques as well as the usage of GPU-accelerated computation techniques is necessary to obtain results in reasonable calculation times.

Using the established framework and solution techniques, the MODIBE model can be used to solve problems of the same class for different functional forms in future projects.