# Ruin probability with Parisian delay for a spectrally negative Lévy risk process - Mathematics > Probability

Ruin probability with Parisian delay for a spectrally negative Lévy risk process - Mathematics > Probability - Download this document for free, or read online. Document in PDF available to download.

Abstract: In this paper we analyze so-called Parisian ruin probability that happenswhen surplus process stays below zero longer than fixed amount of time$\zeta>0$. We focus on general spectrally negative L\-{e}vy insurance riskprocess. For this class of processes we identify expression for ruinprobability in terms of some other quantities that could be possibly calculatedexplicitly in many models. We find its Cram\-{e}r-type andconvolution-equivalent asymptotics when reserves tends to infinity. Finally, weanalyze few explicit examples.

Author: ** Irmina Czarna, Zbigniew Palmowski**

Source: https://arxiv.org/