publication . Article . Other literature type . 2016

Ruin probability with Parisian delay for a spectrally negative L\'evy risk process

Irmina Czarna; Zbigniew Palmowski;
Open Access
  • Published: 14 Jul 2016 Journal: Journal of Applied Probability, volume 48, pages 984-1,002 (issn: 0021-9002, eissn: 1475-6072, Copyright policy)
  • Publisher: Cambridge University Press (CUP)
Abstract
In this paper we analyze so-called Parisian ruin probability that happens when surplus process stays below zero longer than fixed amount of time $\zeta>0$. We focus on general spectrally negative L\'{e}vy insurance risk process. For this class of processes we identify expression for ruin probability in terms of some other quantities that could be possibly calculated explicitly in many models. We find its Cram\'{e}r-type and convolution-equivalent asymptotics when reserves tends to infinity. Finally, we analyze few explicit examples.
Subjects
free text keywords: Statistics, Probability and Uncertainty, Statistics and Probability, General Mathematics, Infinity, media_common.quotation_subject, media_common, Asymptotic analysis, Pure mathematics, Mathematics, Combinatorics, Lévy process, ruin probability, asymptotics, Parisian ruin, risk process, 60J99, 93E20, 60G51
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publication . Article . Other literature type . 2016

Ruin probability with Parisian delay for a spectrally negative L\'evy risk process

Irmina Czarna; Zbigniew Palmowski;