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Ruin probability with Parisian delay for a spectrally negative L\'evy risk process

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  • Irmina Czarna
  • Zbigniew Palmowski
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    Abstract

    In this paper we analyze so-called Parisian ruin probability that happens when surplus process stays below zero longer than fixed amount of time $\zeta>0$. We focus on general spectrally negative L\'{e}vy insurance risk process. For this class of processes we identify expression for ruin probability in terms of some other quantities that could be possibly calculated explicitly in many models. We find its Cram\'{e}r-type and convolution-equivalent asymptotics when reserves tends to infinity. Finally, we analyze few explicit examples.

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    File URL: http://arxiv.org/pdf/1003.4299
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    Bibliographic Info

    Paper provided by arXiv.org in its series Papers with number 1003.4299.

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    Date of creation: Mar 2010
    Date of revision: Apr 2010
    Handle: RePEc:arx:papers:1003.4299

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    Web page: http://arxiv.org/

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    1. Wang, Guojing, 2001. "A decomposition of the ruin probability for the risk process perturbed by diffusion," Insurance: Mathematics and Economics, Elsevier, vol. 28(1), pages 49-59, February.
    2. Bertoin, J. & Doney, R. A., 1994. "Cramer's estimate for Lévy processes," Statistics & Probability Letters, Elsevier, vol. 21(5), pages 363-365, December.
    3. Dufresne, Francois & Gerber, Hans U., 1991. "Risk theory for the compound Poisson process that is perturbed by diffusion," Insurance: Mathematics and Economics, Elsevier, vol. 10(1), pages 51-59, March.
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    Cited by:
    1. Irmina Czarna & Zbigniew Palmowski, 2010. "Dividend problem with Parisian delay for a spectrally negative L\'evy risk process," Papers 1004.3310, arXiv.org, revised Oct 2011.

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