We investigate a banking system subject to repeated macroeconomic shocks and show that without deposit rate control, the banking system collapses with certainty. Any initial level of reserves will delay the collapse but not avoid it. Even without a banking collapse, the economy still converges...

We analyze linear McKean-Vlasov forward-backward SDEs arising in leader-follower games with mean-field type control and terminal state constraints on the state process. We establish an existence and uniqueness of solutions result for such systems in time-weighted spaces as well as a convergence...