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Parisian ruin probability for spectrally negative L\'{e}vy processes

Author

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  • Ronnie Loeffen
  • Irmina Czarna
  • Zbigniew Palmowski

Abstract

In this note we give, for a spectrally negative Levy process, a compact formula for the Parisian ruin probability, which is defined by the probability that the process exhibits an excursion below zero, with a length that exceeds a certain fixed period r. The formula involves only the scale function of the spectrally negative Levy process and the distribution of the process at time r.

Suggested Citation

  • 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.
  • Handle: RePEc:arx:papers:1102.4055
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    File URL: http://arxiv.org/pdf/1102.4055
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    Cited by:

    1. Neofytos Rodosthenous & Hongzhong Zhang, 2017. "Beating the Omega Clock: An Optimal Stopping Problem with Random Time-horizon under Spectrally Negative L\'evy Models," Papers 1706.03724, arXiv.org.
    2. Guérin, Hélène & Renaud, Jean-François, 2017. "On the distribution of cumulative Parisian ruin," Insurance: Mathematics and Economics, Elsevier, vol. 73(C), pages 116-123.
    3. Cheung, Eric C.K. & Wong, Jeff T.Y., 2017. "On the dual risk model with Parisian implementation delays in dividend payments," European Journal of Operational Research, Elsevier, vol. 257(1), pages 159-173.
    4. Wong, Jeff T.Y. & Cheung, Eric C.K., 2015. "On the time value of Parisian ruin in (dual) renewal risk processes with exponential jumps," Insurance: Mathematics and Economics, Elsevier, vol. 65(C), pages 280-290.
    5. 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.
    6. repec:eee:insuma:v:74:y:2017:i:c:p:153-163 is not listed on IDEAS
    7. Albrecher, Hansjörg & Ivanovs, Jevgenijs, 2017. "Strikingly simple identities relating exit problems for Lévy processes under continuous and Poisson observations," Stochastic Processes and their Applications, Elsevier, vol. 127(2), pages 643-656.
    8. Peng, Xiaofan & Luo, Li, 2017. "Finite time Parisian ruin of an integrated Gaussian risk model," Statistics & Probability Letters, Elsevier, vol. 124(C), pages 22-29.
    9. Jean-Franc{c}ois Renaud, 2013. "On the time spent in the red by a refracted L\'evy risk process," Papers 1306.4619, arXiv.org.
    10. repec:spr:queues:v:86:y:2017:i:3:d:10.1007_s11134-017-9529-y is not listed on IDEAS
    11. repec:eee:stapro:v:137:y:2018:i:c:p:157-164 is not listed on IDEAS
    12. Mohamed Amine Lkabous & Irmina Czarna & Jean-Franc{c}ois Renaud, 2016. "Parisian ruin for a refracted L\'evy process," Papers 1603.09324, arXiv.org, revised Mar 2017.
    13. Landriault, David & Li, Bin & Li, Danping & Li, Dongchen, 2016. "A pair of optimal reinsurance–investment strategies in the two-sided exit framework," Insurance: Mathematics and Economics, Elsevier, vol. 71(C), pages 284-294.

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