Conditional equations

[jpfeifer]

1. There is the original paper at https://www.sciencedirect.com/science/article/abs/pii/S0304393214001238
2. In the deterministic model, Dynare will solve the model nonlinearly. Here the max operator is fine.
3. An alternative to the hard constraint in a stochastic model could be a penalty function. See

The Jacobian contains NaNs

Using a penalty function to embed a non-negativity constraint can be done. You might want to take a look at e.g. Kim/Kollmann/Kim (2010) Solving the incomplete market model with aggregate uncertainty using a perturbation method) or dynare.org/wp-repo/dynarewp027.pdf