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A note on Parisian ruin under a hybrid observation scheme

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  • Lkabous, Mohamed Amine

Abstract

In this paper, we study the concept of Parisian ruin under the hybrid observation scheme model introduced by Li et al. (2018). Under this model, the process is observed at Poisson arrival times whenever the business is financially healthy and it is continuously observed when it goes below 0. The Parisian ruin is then declared when the process stays below zero for a consecutive period of time greater than a fixed delay. We improve the result originally obtained in Li et al. (2018) and we compute other fluctuation identities. All identities are given in terms of second-generation scale functions.

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  • Lkabous, Mohamed Amine, 2019. "A note on Parisian ruin under a hybrid observation scheme," Statistics & Probability Letters, Elsevier, vol. 145(C), pages 147-157.
    • Handle: RePEc:eee:stapro:v:145:y:2019:i:c:p:147-157
    DOI: 10.1016/j.spl.2018.09.013
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    References listed on IDEAS

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    1. Li, Yingqiu & Zhou, Xiaowen, 2014. "On pre-exit joint occupation times for spectrally negative Lévy processes," Statistics & Probability Letters, Elsevier, vol. 94(C), pages 48-55.
    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. Lkabous, Mohamed Amine & Czarna, Irmina & Renaud, Jean-François, 2017. "Parisian ruin for a refracted Lévy process," Insurance: Mathematics and Economics, Elsevier, vol. 74(C), pages 153-163.
    4. Mohamed Amine Lkabous & Jean-François Renaud, 2018. "A VaR-Type Risk Measure Derived from Cumulative Parisian Ruin for the Classical Risk Model," Risks, MDPI, vol. 6(3), pages 1-11, August.
    5. 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.
    6. 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.
    7. 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.
    8. 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.
    9. Landriault, David & Li, Bin & Wong, Jeff T.Y. & Xu, Di, 2018. "Poissonian potential measures for Lévy risk models," Insurance: Mathematics and Economics, Elsevier, vol. 82(C), pages 152-166.
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    Cited by:

    1. Mohamed Amine Lkabous, 2019. "Poissonian occupation times of spectrally negative L\'evy processes with applications," Papers 1907.09990, arXiv.org.
    2. David Landriault & Bin Li & Mohamed Amine Lkabous, 2019. "On occupation times in the red of L\'evy risk models," Papers 1903.03721, arXiv.org, revised Jul 2019.
    3. 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.

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