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Parisian ruin probability with a lower ultimate bankrupt barrier

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  • Irmina Czarna

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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  • Irmina Czarna, 2016. "Parisian ruin probability with a lower ultimate bankrupt barrier," Scandinavian Actuarial Journal, Taylor & Francis Journals, vol. 2016(4), pages 319-337, April.
    • Handle: RePEc:taf:sactxx:v:2016:y:2016:i:4:p:319-337
    DOI: 10.1080/03461238.2014.926288
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    Cited by:

    1. Nguyen, Duy Phat & Borovkov, Konstantin, 2023. "Parisian ruin with random deficit-dependent delays for spectrally negative Lévy processes," Insurance: Mathematics and Economics, Elsevier, vol. 110(C), pages 72-81.
    2. Cheung, Eric C.K. & Zhu, Wei, 2023. "Cumulative Parisian ruin in finite and infinite time horizons for a renewal risk process with exponential claims," Insurance: Mathematics and Economics, Elsevier, vol. 111(C), pages 84-101.

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