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

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  • Ronnie Loeffen
  • Irmina Czarna
  • Zbigniew Palmowski
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    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.

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    File URL: http://arxiv.org/pdf/1102.4055
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    Bibliographic Info

    Paper provided by arXiv.org in its series Papers with number 1102.4055.

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    Date of creation: Feb 2011
    Date of revision: Mar 2013
    Publication status: Published in Bernoulli 2013, Vol. 19, No. 2, 599-609
    Handle: RePEc:arx:papers:1102.4055

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    Web page: http://arxiv.org/

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    Cited by:
    1. Jean-Fran\c{c}ois Renaud, 2013. "On the time spent in the red by a refracted L\'evy risk process," Papers 1306.4619, arXiv.org.

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