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A note on Parisian ruin with an ultimate bankruptcy level for Lévy insurance risk processes

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  • Czarna, Irmina
  • Renaud, Jean-François

Abstract

In this short paper, we investigate a definition of Parisian ruin introduced in Czarna (2016), namely Parisian ruin with an ultimate bankruptcy level. We improve the results originally obtained and, moreover, we compute more general Parisian fluctuation identities.

Suggested Citation

  • Czarna, Irmina & Renaud, Jean-François, 2016. "A note on Parisian ruin with an ultimate bankruptcy level for Lévy insurance risk processes," Statistics & Probability Letters, Elsevier, vol. 113(C), pages 54-61.
    • Handle: RePEc:eee:stapro:v:113:y:2016:i:c:p:54-61
    DOI: 10.1016/j.spl.2016.02.018
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    References listed on IDEAS

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    1. Dickson,David C. M., 2016. "Insurance Risk and Ruin," Cambridge Books, Cambridge University Press, number 9781107154605.
    2. David Landriault & Jean-François Renaud & Xiaowen Zhou, 2014. "An Insurance Risk Model with Parisian Implementation Delays," Methodology and Computing in Applied Probability, Springer, vol. 16(3), pages 583-607, September.
    3. Loeffen, Ronnie L. & Renaud, Jean-François & Zhou, Xiaowen, 2014. "Occupation times of intervals until first passage times for spectrally negative Lévy processes," Stochastic Processes and their Applications, Elsevier, vol. 124(3), pages 1408-1435.
    4. Landriault, David & Renaud, Jean-François & Zhou, Xiaowen, 2011. "Occupation times of spectrally negative Lévy processes with applications," Stochastic Processes and their Applications, Elsevier, vol. 121(11), pages 2629-2641, November.
    5. Ronnie Loeffen & Irmina Czarna & Zbigniew Palmowski, 2011. "Parisian ruin probability for spectrally negative L\'{e}vy processes," Papers 1102.4055, arXiv.org, revised Mar 2013.
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    Cited by:

    1. Li, Shu & Zhou, Xiaowen, 2022. "The Parisian and ultimate drawdowns of Lévy insurance models," Insurance: Mathematics and Economics, Elsevier, vol. 107(C), pages 140-160.
    2. Zhang, Aili & Chen, Ping & Li, Shuanming & Wang, Wenyuan, 2022. "Risk modelling on liquidations with Lévy processes," Applied Mathematics and Computation, Elsevier, vol. 412(C).
    3. Lkabous, Mohamed Amine, 2019. "A note on Parisian ruin under a hybrid observation scheme," Statistics & Probability Letters, Elsevier, vol. 145(C), pages 147-157.
    4. Krystecki, Konrad, 2022. "Parisian ruin probability for two-dimensional Brownian risk model," Statistics & Probability Letters, Elsevier, vol. 182(C).
    5. 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.
    6. Mohamed Amine Lkabous, 2019. "A note on Parisian ruin under a hybrid observation scheme," Papers 1907.09993, arXiv.org.

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