On the Cash Balance Problem

The problem of determining the optimal level of a firm's cash balance has been studied by many researchers. Their analyses differ with respect to the assumptions made about both the cost structure faced by the firm and the nature of the flow of funds to the firm. Because of the different methodologies employed by these authors, a proof of the form of the optimum policy only exists for some assumptions about costs and cash flow conditions. Under other conditions, authors have simply assumed the form of the policy and solved for the parameters of that policy. This paper uses a general dynamic programming formulation of the cash balance problem to derive the form of the optimal cash balance problem under different assumptions about transaction costs and the demand for funds. It consists of a review, synthesis, generalization, and in many cases gives a more rigorous derivation of results. Also the nature of the cash balance problem is expanded in the interest of realism, to allow for access to short-term sources of funds.