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A unified approach to ruin probabilities with delays for spectrally negative Lévy processes

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  • Mohamed Amine Lkabous
  • Jean-François Renaud

Abstract

In this paper, we unify two popular approaches for the definition of actuarial ruin with implementation delays, also known as Parisian ruin. Our new definition of ruin includes both deterministic delays and exponentially distributed delays: ruin is declared the first time an excursion in the red zone lasts longer than an implementation delay with a deterministic and a stochastic component. For this Parisian ruin with mixed delays, we identify the joint distribution of the time of ruin and the deficit at ruin, therefore providing generalizations of many results previously obtained, such as in Baurdoux et al. (2016) and Loeffen et al. (in press) for the case of an exponential delay and that of a deterministic delay, respectively.

Suggested Citation

  • Mohamed Amine Lkabous & Jean-François Renaud, 2019. "A unified approach to ruin probabilities with delays for spectrally negative Lévy processes," Scandinavian Actuarial Journal, Taylor & Francis Journals, vol. 2019(8), pages 711-728, September.
    • Handle: RePEc:taf:sactxx:v:2019:y:2019:i:8:p:711-728
    DOI: 10.1080/03461238.2019.1598890
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    Cited by:

    1. Renaud, Jean-François, 2024. "A note on the optimal dividends problem with transaction costs in a spectrally negative Lévy model with Parisian ruin," Statistics & Probability Letters, Elsevier, vol. 206(C).
    2. 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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