EXISTENCE OF OPTIMAL SIMPLE POLICIES FOR DISCOUNTED-COST INVENTORY AND CASH MANAGEMENT IN CONTINUOUS TIME

Formulation of a continuous-time, infinite-horizon, discounted-cost cash management model with both fixed and proportional transactions costs and with linear holding and penalty cost. The culmulative demand for cash by a Wiener process with drift and use the optimal control technique of ″impulse control″ to find sufficient conditions under which an optimal policy exists is modelled. It is shown that these conditions are always met. It is proven that there always exists an optimal policy for the cash management problem and that is policy is of simple form. When the proportional transactions cost of decreasing the cash balance is sufficiently high, it is never optimal to decrease the cash balance. Then the cash management model degenerates to the inventory model.