an:06004673
Zbl 1231.91145
Biffis, Enrico; Kyprianou, Andreas E.
A note on scale functions and the time value of ruin for L??vy insurance risk processes
EN
Insur. Math. Econ. 46, No. 1, 85-91 (2010).
00295222
2010
j
91B30 60G51 60K10
scale functions; ruin; spectrally negative L??vy processes; Gerber-Shiu function; Laplace transform
Summary: We examine discounted penalties at ruin for surplus dynamics driven by a general spectrally negative L??vy 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 [\textit{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.
Zbl 1215.60051