A note on scale functions and the time value of ruin for Lévy insurance risk processes

We examine discounted penalties at ruin for surplus dynamics driven by a general spectrally negative Lévy process; the natural class of stochastic processes which contains many examples of risk processes which have already been considered in the existing literature. Following from the important cont...

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Bibliographic Details
Published in:Insurance, mathematics & economics mathematics & economics, 2010-02, Vol.46 (1), p.85-91
Main Authors: Biffis, Enrico, Kyprianou, Andreas E.
Format: Article
Language:English
Subjects:
Gerber–Shiu function
Insurance
Insurance claims
Laplace transform
Mathematical functions
Risk
Risk assessment
Ruin
Scale analysis
Scale functions
Scale functions Ruin Spectrally negative Levy processes Gerber-Shiu function Laplace transform
Spectrally negative Lévy processes
Stochastic models
Stochastic processes
Studies
Time
Valuation
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Summary:We examine discounted penalties at ruin for surplus dynamics driven by a general spectrally negative Lévy process; the natural class of stochastic processes which contains many examples of risk processes which have already been considered in the existing literature. Following from the important contributions of [Zhou, X., 2005. On a classical risk model with a constant dividend barrier. North Am. Act. J. 95–108] we provide an explicit characterization of a generalized version of the Gerber–Shiu function in terms of scale functions, streamlining and extending results available in the literature.
ISSN:0167-6687
1873-5959
DOI:10.1016/j.insmatheco.2009.04.005