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

2014/10/28 by Kazutoshi Yamazaki, Yamazaki, Kazutoshi
Mathematics · #49J40 #60G51 #93E20 #FOS: Mathematics #Optimization and Control (math.OC) #Probability (math.PR) #math.OC #math.PR #msc:49J40 #msc:60G51 #msc:93E20

paper · pdf · doi:10.48550/arxiv.1410.7490

arxiv created 2015/09/15 · arxiv updated 2015/09/16

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.

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