Risk analysis for a stochastic cash management model with two types of customers

David Perry; Wolfgang Stadje

doi:10.1016/S0167-6687(99)00037-2

Risk analysis for a stochastic cash management model with two types of customers

David Perry, Wolfgang Stadje

Department of Statistics

Research output: Contribution to journal › Article › peer-review

Abstract

A stochastic cash management system is studied in which the cash flow is modeled by the superposition of a Brownian motion with drift and a compound Poisson process with positive and negative jumps for "big" deposits and withdrawals, respectively. We derive explicit formulas for the distributions of the bankruptcy time, the time until bankruptcy or the reaching of a prespecified level, the maximum cash amount in the system, and for the expected discounted revenue generated by the system.

Original language	English
Pages (from-to)	25-36
Number of pages	12
Journal	Insurance: Mathematics and Economics
Volume	26
Issue number	1
DOIs	https://doi.org/10.1016/S0167-6687(99)00037-2
State	Published - 1 Feb 2000

Keywords

Bankruptcy
Brownian motion
Cash management
Compound Poisson process
First-exit time
Maximum cash amount.
Revenue functional

ASJC Scopus subject areas

Statistics and Probability
Economics and Econometrics
Statistics, Probability and Uncertainty

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AB - A stochastic cash management system is studied in which the cash flow is modeled by the superposition of a Brownian motion with drift and a compound Poisson process with positive and negative jumps for "big" deposits and withdrawals, respectively. We derive explicit formulas for the distributions of the bankruptcy time, the time until bankruptcy or the reaching of a prespecified level, the maximum cash amount in the system, and for the expected discounted revenue generated by the system.

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KW - Brownian motion

KW - Cash management

KW - Compound Poisson process

KW - First-exit time

KW - Maximum cash amount.

KW - Revenue functional

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Risk analysis for a stochastic cash management model with two types of customers

Abstract

Keywords

ASJC Scopus subject areas

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