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Applications of factorization embeddings for Lévy processes

Part of: Mathematical economics Stochastic processes

Published online by Cambridge University Press:  01 July 2016

A. B. Dieker
A. B. Dieker*
Affiliation:
CWI Amstredam and University of Twente
*
∗ Current address: University College Cork, BCRI, 17 South Bank, Crosses Green, Cork, Ireland. Email address: [email protected]
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Abstract

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We give three applications of the Pecherskii-Rogozin-Spitzer identity for Lévy processes. First, we find the joint distribution of the supremum and the epoch at which it is ‘attained’ if a Lévy process has phase-type upward jumps. We also find the characteristics of the ladder process. Second, we establish general properties of perturbed risk models, and obtain explicit fluctuation identities in the case that the Lévy process is spectrally positive. Third, we study the tail asymptotics for the supremum of a Lévy process under different assumptions on the tail of the Lévy measure.

Keywords

First factorization identityLévy processperturbed risk modelphase-type jumpruin probability

MSC classification

Secondary: 60G70: Extreme value theory; extremal processes 91B30: Risk theory, insurance
Type
General Applied Probability
Information
Advances in Applied Probability , Volume 38 , Issue 3 , September 2006 , pp. 768 - 791
Copyright
Copyright © Applied Probability Trust 2006 

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