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Discrete time ruin probability with Parisian delay

Author

Listed:
  • Irmina Czarna
  • Zbigniew Palmowski
  • Przemysław Świa̧tek

Abstract

In this paper we evaluate the probability of the discrete time Parisian ruin that occurs when surplus process stays below or at zero at least for some fixed duration of time d>0$ d>0 $. We identify expressions for the ruin probabilities within finite and infinite-time horizon. We also find their light and heavy-tailed asymptotics when initial reserves approach infinity. Finally, we calculate these probabilities for a few explicit examples.

Suggested Citation

  • Irmina Czarna & Zbigniew Palmowski & Przemysław Świa̧tek, 2017. "Discrete time ruin probability with Parisian delay," Scandinavian Actuarial Journal, Taylor & Francis Journals, vol. 2017(10), pages 854-869, November.
    • Handle: RePEc:taf:sactxx:v:2017:y:2017:i:10:p:854-869
    DOI: 10.1080/03461238.2016.1261734
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    Cited by:

    1. Tao Sun & Xinqiu Zhang, 2024. "Laplace Transformation of the Ruin Time for a Risk Model with a Parisian Implementation Delay," Mathematics, MDPI, vol. 12(4), pages 1-12, February.

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