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A note on scale functions and the time value of ruin for Lévy insurance risk processes. (English) Zbl 1231.91145
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 [X. Zhou, N. Am. Actuar. J. 9, No. 4, 95–108 (2005; Zbl 1215.60051)] 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.

##### MSC:
 91B30 Risk theory, insurance (MSC2010) 60G51 Processes with independent increments; Lévy processes 60K10 Applications of renewal theory (reliability, demand theory, etc.)
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##### References:
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