Discrete shocks in Stochastic DSGE with Dynare

Hello dear Dynare users.

I wish to solve a DSGE model with discrete investment shock. It is quite similar to the standard RBC, but the capital motion looks like this:

K_t+1 = (1-delta)K_t + zetai_t.

zeta represents a delivery hazard, so that in the model investment at time t may be delivered at time t+1 (zeta = 1, with probability theta) or not (zeta = 0, with probability (1-theta)). Because zeta (that occure at t+1) is not known at time t when decision on i_t is made, the model is stochastic, not deterministic. Investment cannot get lost for ever, but don’t be concerned on how to track investment because in the full model additional tricks handle this problem. My question is how to specify zeta, (such a bernouilli shock), in Dynare ?

I saw the Drawing from non-normal distributions in model simulation and the Drawing from non-normal distributions(uniform)in simulation discussions. But there seems that the proposed solutions are valid only in first order approximation, which would be treating my representation as a deterministic model. Any help would be highly appreciated.

Thank you.

From what you describe, it sounds as if perturbation-based techniques will not be able to handle this problem. Thus, you cannot use Dynare, but rather need some global solution technique.