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A STOCHASTIC CLEARING MODEL WITH A BROWNIAN AND A COMPOUND POISSON COMPONENT

Published online by Cambridge University Press:  07 January 2003

Offer Kella ,
David Perry  and
Wolfgang Stadje
Offer Kella
Affiliation:
Department of Statistics, The Hebrew University of Jerusalem, Mount Scopus, Jerusalem 91905, Israel, E-mail: mskella@mscc.huji.ac.il
David Perry
Affiliation:
Department of Statistics, University of Haifa, Haifa 31905, Israel, E-mail: dperry@stat.haifa.ac.il
Wolfgang Stadje
Affiliation:
Department of Mathematics and Computer Science, University of Osnabrück, 49069 Osnabrück, Germany, E-mail: wolfgang@mathematik.uni-osnabrueck.de
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Abstract

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We consider a stochastic input–output system with additional total clearings at certain random times determined by its own evolution (and specified by a controller). Between two clearings, the stock level process is a superposition of a Brownian motion with drift and a compound Poisson process with positive jumps, reflected at zero. We introduce meaningful cost functionals for this system and determine them explicitly under several (classical and new) clearing policies.

Type
Research Article
Information
Probability in the Engineering and Informational Sciences , Volume 17 , Issue 1 , January 2003 , pp. 1 - 22
Copyright
© 2003 Cambridge University Press