A diffusion approximation model for managing cash in firms: An alternative approach to the Miller–Orr model

This article considers a cash management problem of a typical business firm in a “two-asset” setting, namely, the firm's cash balance and a portfolio of assets such as treasury bills, commercial papers, etc. From time to time, firms will have to transfer money from one asset account to the other by selling or buying securities to bring the cash balance to a suitable level (return point). These transactions are made when the cash balance reaches the lower or the upper control limits set by the firm. We use the diffusion approximation technique to obtain the probability density function of the daily cash balance and the optimal values for the return point and the upper control limit which minimize the daily cost of managing the cash. Numerical results show that the proposed model is superior to the original model proposed by Miller and Orr in 1966 known as the Miller–Orr model. The proposal can be regarded as a more generalized model which relaxes most of the restrictive assumptions made in the Miller–Orr model.