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On series expansions for scale functions and other ruin-related quantities
Authors:David Landriault  Gordon E Willmot
Institution:1. Department of Statistics and Actuarial Science, University of Waterloo, Waterloo, Ontario, Canadadlandria@uwaterloo.ca;3. Department of Statistics and Actuarial Science, University of Waterloo, Waterloo, Ontario, Canada
Abstract:ABSTRACT

In this note, we consider a nonstandard analytic approach to the examination of scale functions in some special cases of spectrally negative Lévy processes. In particular, we consider the compound Poisson risk process with or without perturbation from an independent Brownian motion. New explicit expressions for the first and second scale functions are derived which complement existing results in the literature. We specifically consider cases where the claim size distribution is gamma, uniform or inverse Gaussian. Some ruin-related quantities will also be re-examined in light of the aforementioned results.
Keywords:Scale function  spectrally negative Lévy process  (perturbed) compound Poisson risk process  ruin probability  Laplace transform of the time to ruin
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