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I don't know your model well enough, so you are the one who needs to figures this out based on economic intuition. In particular you need to think about the timing convention in your model.

The question which debt stock is predetermined is answered by considering when their value is determined. For example, when you buy a risk-free bond today at price R^(-1) you know that the debt stock one period later will be B=1. It does not matter that markets need to adjust at time t+1 to clear the debt market. That only means demand needs to adjust to a given supply

Hello,

thanks a lot for your help.

After thinking about it, I don't think I have any predetermined stock of debt in my model because patient households choose what they want to lend at the same time firms and impatient households choose what they want to borrow and then the debt market clears such that the total amount lent by patient households is split between firms and impatient households. This all occurs in the same period.

However, the decision problem of impatient households might not be very standard and I am wondering whether this could be what makes the Blanchard-Kahn conditions not satisfied in my model. Impatient households can borrow from patient households and they can save money by buying risky stocks to firms. Does that make the borrowing rate not predetermined as there is some risk on impatient households' savings ?
As for firms, they can borrow from patient households and issue stocks.
I do not allow for default in my model. But I am not sure whether my borrowing rate should be seen as a risk-free rate (known in the previous period before being paid) or not.

In the Iacoviello paper "Financial Business Cycles" https://www2.bc.edu/~iacoviel/research_files/FBC.pdf (2014), I don't understand why the deposit rate paid by banks to patient households is predetermined and why, on the contrary, the lending rate paid by firms to banks on their loans is not predetermined. Do I have something similar here ?

Thanks again

It might be, but I am no expert in this literature. You need to understand the economic intuition behind your modeling approach. It will deliver the answer to the correct timing that makes the model solve.