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Parisian Ruin with Erlang Delay and a Lower Bankruptcy Barrier

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  • Esther Frostig

    (Haifa University)

  • Adva Keren-Pinhasik

    (Haifa University)

Abstract

Parisian ruin occurs once the surplus stays continuously below zero for a given period. We consider the spectrally negative Lévy risk process where ruin is declared either at the first time that the reserve stays continuously below zero for an exponentially or mixed Erlang distributed random variable, or once it reaches a given negative threshold. We consider the Laplace transform of the time to ruin and the Laplace transform of the time that the process is negative.

Suggested Citation

  • Esther Frostig & Adva Keren-Pinhasik, 2020. "Parisian Ruin with Erlang Delay and a Lower Bankruptcy Barrier," Methodology and Computing in Applied Probability, Springer, vol. 22(1), pages 101-134, March.
    • Handle: RePEc:spr:metcap:v:22:y:2020:i:1:d:10.1007_s11009-019-09693-w
    DOI: 10.1007/s11009-019-09693-w
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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. Frostig, Esther & Pitts, Susan M. & Politis, Konstadinos, 2012. "The time to ruin and the number of claims until ruin for phase-type claims," Insurance: Mathematics and Economics, Elsevier, vol. 51(1), pages 19-25.
    3. Asmussen, Soren & Avram, Florin & Usabel, Miguel, 2002. "Erlangian Approximations for Finite-Horizon Ruin Probabilities," ASTIN Bulletin, Cambridge University Press, vol. 32(2), pages 267-281, November.
    4. Loeffen, R. & Palmowski, Z. & Surya, B.A., 2018. "Discounted penalty function at Parisian ruin for Lévy insurance risk process," Insurance: Mathematics and Economics, Elsevier, vol. 83(C), pages 190-197.
    5. Dassios, Angelos & Wu, Shanle, 2009. "On barrier strategy dividends with Parisian implementation delay for classical surplus processes," Insurance: Mathematics and Economics, Elsevier, vol. 45(2), pages 195-202, October.
    6. 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.
    7. Dassios, Angelos & Wu, Shanle, 2008. "Parisian ruin with exponential claims," LSE Research Online Documents on Economics 32033, London School of Economics and Political Science, LSE Library.
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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.

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