The MORIBE model is a framework which allows for the incorporation of stochastic elements in the dynamic decision making of different economic actors.

We formulate the dynamic and stochastic optimization problems in the form of stochastic Bellman equations, what allows us to use establish theory and numerical methods to tackle the problems. However, as multiple risk factors and large numbers of state and decision variables would require tremendous computational efforts, we develop new methods extending the standard solution techniques of value function iteration. We use a combination of several different optimization techniques as well as the usage of GPU-accelerated computation techniques to obtain results in reasonable computation times.

The MORIBE framework allows us to model the behaviour of different economic actors in the face of different types of shocks. So far we have used the MORIBE model for

• the modelling of household behaviour in the face of natural disaster risk,
• the modelling of land-use decisions by farmers under stochastic development of the prices of agricultural goods.

## Modelling household behaviour in the face of disaster risk

In this work we propose 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.

We obtain a complex decision framework illustrated in the flow chart below, which can be mathematically formulated with a Bellman equation. For more information on this project see the themes page or the working paper "Should I stay or should I go: Modelling disaster risk behaviour using a dynamic household level approach" by Freiberger, Hoffmann and Prskawetz (2024).

The code for the numerical solution of the model can be found on GitHub.

## Modelling land-use decision under stochastic prices for agricultural goods

In the PVARGLOBIOM project we use the MORIBE to extend the GLOBIOM framework with a focus on the land-use decisions in the face of price shocks to agricultatural goods. Farmers can decide to increase or decrease the size of their agricultural land, but also to change the cultivation type. In the process of maximizing expected long-run profits with their decisions on land-use as well as agricultural efforts, farmers not only face the stochastic nature of the prices for agricultural products, but also investment limitations due to borrowing constraints. The project is currently work in progress, but the code for the numerical solution will be made available on GitHub.