Parisian ruin probability with a lower ultimate bankrupt barrier

Irmina Czarna

Scandinavian Actuarial Journal, 2016, vol. 2016, issue 4, 319-337

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.

Date: 2016
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DOI: 10.1080/03461238.2014.926288

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