Cash Management and Control Band Policies for Spectrally One-sided Levy Processes

We study the control band policy arising in the context of cash balance management. A policy is specified by four parameters (d,D,U,u). The controller pushes the process up to D as soon as it goes below d and pushes down to U as soon as it goes above u, while he does not intervene whenever it is within the set (d, u). We focus on the case when the underlying process is a spectrally one-sided Levy process and obtain the expected fixed and proportional controlling costs as well as the holding costs under the band policy.