Indicator function on a general equilibrium model

Hello everyone, I’m a newcomer in this society and I hope you can help me out.

I have a bunch of equations that conform a general equilibrium model.
One of the equations contains an indicator function (takes the value of 1 if something happens, 0 otherwise).
Specifically, the activation of this function (that takes the value of 1) depends on a variable of the model. More specifically, the function is equal to 1 if this variable is less than a threshold, 0 if it is larger that the threshold.
Is that possible to code?
What are the implications on the nature of the model? It would have to be deterministic or stochastic?
Can you recommend me a text book to check the implications of having an indicator function on a general equilibrium model?

I really hope you can help me out, thank you in advance fellows.

Indicator functions are just like any other function. They can be used in general equilibrium models, both stochastic and deterministic.

The tricky issue comes when you want to solve your general equilibrium model. An indicator function typically introduces kinks at the point where the indicator switches. This implies that the model is not differentiable at this point. Any derivative-based solution will fail. Dynare uses perturbation, which is based on derivatives to solve stochastic models. Thus, you cannot solve stochastic models with indicator functions in Dynare. You could solve a deterministic version.
If you want to go for a stochastic version with indicator functions, you would need to do e.g. value function or policy function iteration (discrete state space methods).

There is no literature for the special case of indicator functions as they are just a special case of non-differentiable functions.