A note on the optimal control of a cash balance problem

Charles Tapiero, Dror Zuckerman

Research output: Contribution to journalArticle

Abstract

This paper provides an analytical solution to a cash management problem when cash income and demand are described by Compound Poisson processes. The paper generalizes past results in the cash management literature to arbitrary income and demand distribution functions. Further, our results can be applied as well in the area of banking. Throughout the paper we restrict attention to the family of control barrier policies. These consist in hedging cash up to a critical level and investing all incoming cash exceeding this level. We employ a long-run average cost criterion to determine an optimal control barrier. A diffusion approximation of the cash level process (income less demand) is used to obtain a simpler expression for the average cost and to yield a closed form solution to the optimal control barrier. For demonstration purposes, an example is resolved.

Original languageEnglish (US)
Pages (from-to)345-352
Number of pages8
JournalJournal of Banking and Finance
Volume4
Issue number4
DOIs
StatePublished - 1980

Fingerprint

Cash
Optimal control
Income
Average cost
Cash management
Distribution function
Analytical solution
Banking
Closed-form solution
Hedging
Diffusion approximation
Investing
Compound Poisson process

ASJC Scopus subject areas

  • Economics and Econometrics
  • Finance

Cite this

A note on the optimal control of a cash balance problem. / Tapiero, Charles; Zuckerman, Dror.

In: Journal of Banking and Finance, Vol. 4, No. 4, 1980, p. 345-352.

Research output: Contribution to journalArticle

@article{7b28d1c17d8a45e6ab9f138dba8f7ab2,
title = "A note on the optimal control of a cash balance problem",
abstract = "This paper provides an analytical solution to a cash management problem when cash income and demand are described by Compound Poisson processes. The paper generalizes past results in the cash management literature to arbitrary income and demand distribution functions. Further, our results can be applied as well in the area of banking. Throughout the paper we restrict attention to the family of control barrier policies. These consist in hedging cash up to a critical level and investing all incoming cash exceeding this level. We employ a long-run average cost criterion to determine an optimal control barrier. A diffusion approximation of the cash level process (income less demand) is used to obtain a simpler expression for the average cost and to yield a closed form solution to the optimal control barrier. For demonstration purposes, an example is resolved.",
author = "Charles Tapiero and Dror Zuckerman",
year = "1980",
doi = "10.1016/0378-4266(80)90013-8",
language = "English (US)",
volume = "4",
pages = "345--352",
journal = "Journal of Banking and Finance",
issn = "0378-4266",
publisher = "Elsevier",
number = "4",

}

TY - JOUR

T1 - A note on the optimal control of a cash balance problem

AU - Tapiero, Charles

AU - Zuckerman, Dror

PY - 1980

Y1 - 1980

N2 - This paper provides an analytical solution to a cash management problem when cash income and demand are described by Compound Poisson processes. The paper generalizes past results in the cash management literature to arbitrary income and demand distribution functions. Further, our results can be applied as well in the area of banking. Throughout the paper we restrict attention to the family of control barrier policies. These consist in hedging cash up to a critical level and investing all incoming cash exceeding this level. We employ a long-run average cost criterion to determine an optimal control barrier. A diffusion approximation of the cash level process (income less demand) is used to obtain a simpler expression for the average cost and to yield a closed form solution to the optimal control barrier. For demonstration purposes, an example is resolved.

AB - This paper provides an analytical solution to a cash management problem when cash income and demand are described by Compound Poisson processes. The paper generalizes past results in the cash management literature to arbitrary income and demand distribution functions. Further, our results can be applied as well in the area of banking. Throughout the paper we restrict attention to the family of control barrier policies. These consist in hedging cash up to a critical level and investing all incoming cash exceeding this level. We employ a long-run average cost criterion to determine an optimal control barrier. A diffusion approximation of the cash level process (income less demand) is used to obtain a simpler expression for the average cost and to yield a closed form solution to the optimal control barrier. For demonstration purposes, an example is resolved.

UR - http://www.scopus.com/inward/record.url?scp=49149144703&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=49149144703&partnerID=8YFLogxK

U2 - 10.1016/0378-4266(80)90013-8

DO - 10.1016/0378-4266(80)90013-8

M3 - Article

VL - 4

SP - 345

EP - 352

JO - Journal of Banking and Finance

JF - Journal of Banking and Finance

SN - 0378-4266

IS - 4

ER -