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

Reference:

Biffis, E. and Kyprianou, A. E., 2010. A note on scale functions and the time value of ruin for Levy insurance risk processes. Insurance Mathematics & Economics, 46 (1), pp. 85-91.

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Official URL:

http://dx.doi.org/10.1016/j.insmatheco.2009.04.005

Abstract

We examine discounted penalties at ruin for Surplus dynamics driven by a general spectrally negative Levy 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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