Subexponential loss rate asymptotics for Lévy processes

Subexponential loss rate asymptotics for Lévy processes

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Article ID: iaor20112021
Volume: 73
Issue: 1
Start Page Number: 91
End Page Number: 108
Publication Date: Feb 2011
Journal: Mathematical Methods of Operations Research
Authors:
Keywords: random walk
Abstract:

We consider a Lévy process reflected in barriers at 0 and K > 0. The loss rate is the mean of the local time at K at time 1 when the process is started in stationarity, and is a natural continuous‐time analogue of the stationary expected loss rate for a reflected random walk. We derive asymptotics for the loss rate when K tends to infinity, when the mean of the Lévy process is negative and the positive jumps are subexponential. In the course of this derivation, we achieve a formula, which is a generalization of the celebrated Pollaczeck‐Khinchine formula.

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