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Parisian ruin with random deficit-dependent delays for spectrally negative Lévy processes

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  • Nguyen, Duy Phat
  • Borovkov, Konstantin

Abstract

We consider an interesting natural extension to the Parisian ruin problem under the assumption that the risk reserve dynamics are given by a spectrally negative Lévy process. The distinctive feature of this extension is that the distribution of the random implementation delay windows' lengths can depend on the deficit at the epochs when the risk reserve process turns negative, starting a new negative excursion. This includes the possibility of an immediate ruin when the deficit hits a certain subset. In this general setting, we derive a closed-form expression for the Parisian ruin probability and the joint Laplace transform of the Parisian ruin time and the deficit at ruin.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:insuma:v:110:y:2023:i:c:p:72-81
    DOI: 10.1016/j.insmatheco.2023.02.001
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    References listed on IDEAS

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    More about this item

    Keywords

    Parisian ruin; Random delay; Lévy process; Scale function; Laplace transform of the ruin time;
    All these keywords.

    JEL classification:

    • C65 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Miscellaneous Mathematical Tools

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