A Model for Cash Balance Management

A model for minimizing the average cash balance subject to a constraint on the probability of stock-out is presented. The cash balance is described as an inventory process that changes because of deterministic and stochastic events. Recursive systems of equations are given to find (1) the distribution function of the cash level at any time and (2) the probability that all demands during some time interval are met. Then we examine the problem: minimize the expected time average cash balance subject to the condition that the probability that all demands are satisfied is at least some given number. It is shown that the optimal policy has a very simple form, which can be expressed verbally as, "never have any more cash on hand than is necessary to satisfy the constraint."