The Stochastic Cash Balance Problem with Average Compensating-Balance Requirements

We consider the problem of managing two assets, cash and an earning asset, when net cash flows are stochastic and when there are transfer costs for transferring assets from one form to the other. Previous work on the stochastic cash-balance problem has assumed holding costs for holding excess cash and penalty costs for holding insufficient cash, with these costs assessed per period (the same period in which there is a single decision or transfer opportunity and a single random cash flow). This formulation is appropriate when a firm faces minimum (or zero) compensating-balance requirements, but not when the compensating-balance requirement involves an average deposit balance over a number of decision periods. A dynamic programming model is presented which appropriately represents the relevant cost function for a firm facing an average compensating-balance requirement. The dynamic programming solution to a numerical example is compared to that of a static two-sided (s, S) policy; the optimal dynamic programming solution represents an 18% reduction in relevant costs in the example.