Note—The Stochastic Cash Balance Problem with Charges Levied Against the Balance

Abstract

The finite horizon cash balance problem with charges levied against the cash balance is considered. Conditions, sufficient to show that a two-sided ( s, S ) policy is optimal, are given. We consider transactions cost functions which include no fixed costs, and are linear in the amount of change. Only a reinterpretation of an earlier formulation is required when transactions costs are levied against the balance. When penalty charges are so levied, we require the penalty cost function to be convex, non-negative, and include no charge on a zero ending balance.