Risk analysis for a stochastic cash manangement model with two type of customers
type: Item
instance of: scholarly article
title: Risk analysis for a stochastic cash manangement model with two type of customers
zbMATH Open document ID: 0990.91028
DOI: 10.1016/S0167-6687(99)00037-2
author: David Perry
author: Wolfgang Stadje
published in: Insurance Mathematics \& Economics
publication date: 2002-05-13T00:00:00Z
review text: The authors study the risk analysis of a stochastic cash management model possessing two types of customers: many ``small'' customers, frequently depositing and withdrawing small amounts of money, and a few ``big'' ones causing big upward or downward jumps in the amount of cash held by the system. Accordingly, the total amount of cash in the system is modeled as a sum of two independent components, a Brownian motion with drift plus a compound Poisson process with (positive or negative) exponential jumps, such that the total drift of the cash flow is negative. Making use of some martingale arguments for stochastic storage processes with Lévy input due to \textit{O. Kella} and \textit{W. Whitt} [J. Appl. Probab. 29, 396-403 (1992; Zbl 0761.60065)], the authors derive explicit formulae for the Laplace transforms of some key system characteristics such as e.g. the time to bankruptcy, the maximum amount of cash before bankruptcy, or the expected discounted revenue generated by the system. Possible extensions to models with phase-type or hyperexponential jumps are also discussed.
Mathematics Subject Classification ID: 91B30
Mathematics Subject Classification ID: 91B28
Mathematics Subject Classification ID: 60K25
zbMATH DE Number: 1441570
zbMATH Keywords: bankruptcy time
zbMATH Keywords: maximum cash amount
zbMATH Keywords: revenue functional
zbMATH Keywords: risk analysis
zbMATH Keywords: stochastic cash management
zbMATH Keywords: Brownian motion
zbMATH Keywords: compound Poisson process
reviewed by: J. G. Steinebach
MaRDI profile type: Publication
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full work available at URL: s0167-6687(99)00037-2
OpenAlex ID: W2043281902
Wikidata QID: Q128109168
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description: scientific article; zbMATH DE number 1441570