Forlati and Lambertini (2011) timing issue

Dear all,
I’ve been trying to solve a simplified version of Forlati and Lambertini (2011) paper, but I find the timing somewhat confusing. I guess this is a general question regarding the CSV (BGG) framework.

So in this paper the mortgage rate ensures that the borrowing constraint holds not just ex-ante, but also ex-post. So for me the borrowing constraint has to hold contemporaneously. All the FL2011 mod files I’ve seen here have it in expectation terms, but I don’t think that’s correct.

Then another confusing equation is borrowers’ FOC w.r.t. omegabar, i.e. the default cut-off criterion. FL(2011) mention that it also has to hold state by state and not in expectation terms. But if the decision is made in time “t”, how can that be? And in any case, if both the collateral constraint and the FOC w.r.t. omegabar hold contemporaneously, the rank criterion isn’t satisfied and the model breaks down. Please find attached both the paper and the code. Any ideas are welcome.
steady_equations.m (1.6 KB)
changeAndSaveFunction.m (524 Bytes)
changeAndSaveScript.m (135 Bytes)

model_endog.mod (1.9 KB)
run_model.m (169 Bytes)
solve_steady.m (912 Bytes)