Structural properties of reflected Lévy processes

L.N. Andersen, M.R.H. Mandjes

Research output: Book/ReportReportAcademic

Abstract

This paper considers a number of structural properties of reflected Lévy processes, where both onesided reflection (at 0) and two-sided reflection (at both 0 and K > 0) are examined. With Vt being the position of the reflected process at time t, we focus on the analysis of ¿(t) := EVt and ¿(t) := VarVt. We prove that for the one- and two-sided reflection we have ¿(t) is increasing and concave, whereas for the one-sided reflection we also show that ¿(t) is increasing. In most proofs we first establish the claim for the discrete-time counterpart (that is, a reflected random walk), and then we use a limiting argument. A key step in our proofs for the two-sided reflection is a new representation of the position of the reflected process in terms of the driving Lévy process.
Original languageEnglish
Place of PublicationAmsterdam
PublisherCentrum voor Wiskunde en Informatica
Number of pages19
Publication statusPublished - 2008

Publication series

NameCWI Report
VolumePNA-R0814

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