Parisian ruin probability with a lower ultimate bankrupt barrier |
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Authors: | Irmina Czarna |
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Institution: | 1. Department of Mathematics, University of Wroc?aw, Wroc?aw, Poland.czarna@math.uni.wroc.pl |
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Abstract: | The paper deals with a ruin problem, where there is a Parisian delay and a lower ultimate bankrupt barrier. In this problem, we will say that a risk process get ruined when it stays below zero longer than a fixed amount of time ζ > 0 or goes below a fixed level ?a. We focus on a general spectrally negative Lévy insurance risk process. For this class of processes, we identify the Laplace transform of the ruin probability in terms of so-called q-scale functions. We find its Cramér-type and convolution-equivalent asymptotics when reserves tends to infinity. Finally, we analyze few explicit examples. |
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Keywords: | Lévy process risk process ruin probability asymptotics Parisian ruin |
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