4. [liquidity management with rollover risks, in Final 2018} Consider the bank's liquidity management problem in a three-period model. t period [1, the bank's liabilities consist of deposits D, borrowing from the central bank 3 and paid-in capital E. The bank's problem is to allocate funds over reserves C and loans 1. to maximize expected bank's prots at period 2. Deposits and harming from the central bank do not incur interests. Loans L pay net interest rate r;_ at period 2. Reserves pay ti net interest rate. The reserve requirement ratio is It. At period 1, the bank faces to x D deposit withdrawals, of which to is drawn from the uniform distribution over [their] with 1