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Risk Theory with the Generalized Inverse Gaussian Lévy Process

Published online by Cambridge University Press:  17 April 2015

Manuel Morales
Manuel Morales*
Affiliation:
Department of Mathematics and Statistics, York University, N520 Ross Building, 4700 Keele St., Toronto, Ontario M3J 1P3 – CANADA, E-mail: mmorales@yorku.ca, Phone: (416) 736 2100 ext 33768
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Abstract

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Dufresne et al. (1991) introduced a general risk model defined as the limit of compound Poisson processes. Such model is either a compound Poisson process itself or a strictly increasing Lévy process. Their construction is based on a non-negative non-increasing function Q that governs the jumps of the process. This function, it turns out, is the tail of the Lévy measure of the process. We discuss an illustration of their model using a generalized Inverse Gaussian (GIG) Lévy process. This increasing Lévy process has the gamma and the inverse Gaussian process as particular cases. Although mathematically more complex, the GIG Lévy process keeps some of the nice properties of the simpler gamma process.

Keywords

Risk TheoryRuin ProbabilitiesLévy ProcessGamma ProcessGeneralized Inverse Gaussian Process
Type
Articles
Information
ASTIN Bulletin: The Journal of the IAA , Volume 34 , Issue 2 , November 2004 , pp. 361 - 377
Copyright
Copyright © ASTIN Bulletin 2004

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