I am trying to solve a capital requirements model based on a recent paper by Mendicino et al. (2020, JME) which is based on a BGG (1999) style framework.

In the mod file that I have attached, I am solving this model with aggregate uncertainty, but abstracting from nominal rigidities, monetary policy and household household capital holdings. I additionally attach a file with the variable and parameter definitions and the equilibrium conditions of my model.

I have checked the equations many many times and also cross-checked the timing of variables against a similar older paper of the authors for which they provide code and timing seems to be correct to me.

Nonetheless, I keep running into a BK condition error, having no stable equilibrium. I can get around this by arbitrarily specifying one of the auxiliary variables as (+1) instead of present, but my understanding is that this is indeed inappropriate.

Is there anything you can see in the mod file that seems suspicious?

Could you tell me explicitly why or where you think I am being inconsistent in the timing for capital as I am exactly following the paper in capital timing?

Equation (24) clearly uses the stock at the beginning of period notation where you would take the derivative with respect to K_{t+1}. But in (12), you take the FOC with respect to K_t, which would be the case with a stock at the end of period notation.

Yes, I see that this is indeed unfortunately written in the PDF, my apologies for that. However in the accompanying mod file, (24) is written differently using end of period notation for capital as it should be the case in this model.

I saw that the mod-file is different, but given that the derivation seems to have been buggy, I would recommend rechecking everything. Pay particular focus to what is predetermined.
You may also want to use Dynare’s \LaTeX-capabilities to augment debugging.