Optimal bank and borrower decisions under uncertainty

The dissertation analyzes models of a retail bank, a commercial borrower at the bank, and the interaction of bank and borrower.; The matching book problem is a management problem faced by every retail bank as it balances the term structures of its assets and liabilities. It can either eliminate most of its interest risk with appropriate options, or it can utilize its expertise in its core business and seek extraordinary profits. This research concerns a bank with the latter goal. The bank's decision variables are the amounts of deposits and loans that it is willing to make at various maturities, the dividend pay out and the amount of cash reserves. This research investigates several dynamic stochastic models of the bank's matching book problem. One desirable feature in such models would be that some customers might elect to pay off their long-term loans before maturity. In order to devise credible aggregate models of prepayment behavior, we analyze a dynamic stochastic prepayment model from the borrower's point of view.; In the second essay, the borrower meets random cash needs via multi-period loans from the bank, but fluctuations in interest rates may justify paying off some outstanding loan before they mature. The objective is to minimize the expected present value of the interest and prepayment penalties paid to the bank. We characterize optimal prepayment decision rules and discuss computational issues.; The third part of the essay describes properties of a sequential game model in which the borrower's cash needs and prepayment decisions affect the bank's liquidity, and the bank meets its cash needs with demand deposits. This results in a sequential game with a Stackelberg structure in which the borrower decides each period how much to prepay and how much more to borrow, and the bank decides on the amount of demand deposits which it should seek. By exploiting results in the first part of the talk, we characterize the bank's portion of an equilibrium point. The results depend on the nature of the liquidity constraint that constrains the bank.