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XII Symposium of Probability and Stochastic ProcessesAsymptotic Results for the Severity and Surplus Before Ruin for a Class of Lévy Insurance Processes

XII Symposium of Probability and Stochastic Processes: Asymptotic Results for the Severity and... [We investigate a classical two-sided jumps risk process perturbed by a spectrally negative α-stable process, in which the gain size distribution has a rational Laplace transform. We consider three classes of light- and heavy-tailed claim size distributions. We obtain the asymptotic behaviors of the ruin probability and of the joint tail of the surplus prior to ruin and the severity of ruin, for large values of the initial capital. We also show that our asymptotic results are sharp. This extends our previous work (Kolkovska and Martín-González, Gerber-Shiu functionals for classical risk processes perturbed by an α-stable motion. Insur Math Econ 66:22–28, 2016).] http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png

XII Symposium of Probability and Stochastic ProcessesAsymptotic Results for the Severity and Surplus Before Ruin for a Class of Lévy Insurance Processes

Part of the Progress in Probability Book Series (volume 73)
Editors: Hernández-Hernández, Daniel; Pardo, Juan Carlos; Rivero, Victor
Kolkovska, Ekaterina T.; Martín-González, Ehyter M.
XII Symposium of Probability and Stochastic Processes — Jun 27, 2018
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References (13)

Publisher
Springer International Publishing
Copyright
© Springer International Publishing AG, part of Springer Nature 2018
ISBN
978-3-319-77642-2
Pages
107 –134
DOI
10.1007/978-3-319-77643-9_3
Publisher site
See Chapter on Publisher Site

Abstract

[We investigate a classical two-sided jumps risk process perturbed by a spectrally negative α-stable process, in which the gain size distribution has a rational Laplace transform. We consider three classes of light- and heavy-tailed claim size distributions. We obtain the asymptotic behaviors of the ruin probability and of the joint tail of the surplus prior to ruin and the severity of ruin, for large values of the initial capital. We also show that our asymptotic results are sharp. This extends our previous work (Kolkovska and Martín-González, Gerber-Shiu functionals for classical risk processes perturbed by an α-stable motion. Insur Math Econ 66:22–28, 2016).]

Published: Jun 27, 2018

Keywords: Two-sided risk process; Stable process; Ruin probability; Severity of ruin; Surplus before ruin; Asymptotic ruin probability; 60G51

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