A Stochastic Cash Balance Model with Two Sources of Short-Term Funds

IN A RECENT PAPER G. D. Eppen and E. F. Fama [3] develop a discrete cash balance model with proportional transaction costs using a dynamic programming formulation (denoted as the EF-model). The uncontrollable cash flows are assumed to have a discrete stationary probability distribution. The cash balance is adjusted by selling or buying some earning assets, presumably short-term marketable securities. The model assumes that the cash balance may become negative, i.e., the firm operates under an automatic bank account overdraft situation as found in many countries-which, however, is not the usual situation in the United States. If Bn denotes the cash balance carried forward from the previous period, and Un and D. denote return points for period n, the optimal solution of the EF-model can be characterized as follows: if Bn < U.: increase the cash balance to Un if Un < Bn < D.: do not change the cash balance if Dn < Bn: decrease the cash balance to Dn. This paper proposes to generalize the EF-model to cash balance situations where 1. No bank account overdrafts are possible. Attempts to overdraw the account result in a cash shortage cost. 2. Two different sources of short-term funds are available each with different transaction costs. 3. The probability distribution of cash flows is not necessarily stationary. 4. The length of the cash balance review periods may vary from period to period.'