Self-fulfilling Debt Dilution in Discrete Time
The setup follows the setup in Aguiar and Amador (19), Self-fulfilling Debt Dilution: Maturity and Multiplicity in Debt Models.
This confirms the validity of the equilibrium constructions in that paper but now in an environment with discrete time and concave utility.
It also shows that iterating backwards from a finite horizon, $T$, does not provide a way to select among the multiple equilibria. We provide examples where this procedure converges to either the savings or the borrowing equilibrium, depending on the parameter specification.
See the jupyter notebook "simulating_two_states.ipynb" for the simulation results.