A note on scale functions and the time value of ruin for Lévy insurance risk processes |
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Authors: | Enrico Biffis |
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Institution: | a Imperial College Business School, Imperial College London, South Kensington Campus, SW7 2AZ, United Kingdom b Department of Mathematical Sciences, University of Bath, Claverton Down, Bath, BA2 7AY, United Kingdom |
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Abstract: | 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. |
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Keywords: | Scale functions Ruin Spectrally negative Lé vy processes Gerber-Shiu function Laplace transform |
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