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

TL;DR

This paper analyzes a cash management control policy for spectrally one-sided Levy processes, deriving cost functions and optimal parameters for effective cash balance regulation.

Contribution

It introduces a novel analysis of control band policies specifically tailored for spectrally one-sided Levy processes, including explicit cost calculations.

Findings

Explicit formulas for fixed and proportional controlling costs.

Characterization of optimal control band parameters.

Insights into cash management efficiency with Levy processes.

Abstract

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.