Landriault, David; Willmot, Gordon E. On series expansions for scale functions and other ruin-related quantities. (English) Zbl 1447.91142 Scand. Actuar. J. 2020, No. 4, 292-306 (2020). Summary: 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. Cited in 2 ReviewsCited in 6 Documents MSC: 91G05 Actuarial mathematics 60G51 Processes with independent increments; Lévy processes Keywords:scale function; spectrally negative Lévy process; (perturbed) compound Poisson risk process; ruin probability; Laplace transform of time to ruin PDFBibTeX XMLCite \textit{D. Landriault} and \textit{G. E. Willmot}, Scand. Actuar. J. 2020, No. 4, 292--306 (2020; Zbl 1447.91142) Full Text: DOI References: [1] Abramowitz, M.; Stegun, I. A., Handbook of mathematical functions (1970), New York: Dover, New York [2] Albrecher, H.; Renaud, J. F.; Zhou, X., A Lévy insurance risk process with tax, Journal of Applied Probability, 45, 2, 363-375 (2008) · Zbl 1144.60032 [3] Albrecher, H.; Ivanovs, J.; Zhou, X., Exit identities for Lévy processes observed at Poisson arrival times, Bernoulli, 22, 3, 1364-1382 (2016) · Zbl 1338.60125 [4] Avram, F.; Kyprianou, A. E.; Pistorius, M. 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