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The Parisian and ultimate drawdowns of Lévy insurance models

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  • Li, Shu
  • Zhou, Xiaowen

Abstract

In this paper, inspired by the ideas of Parisian ruin and ultimate bankruptcy, we introduce two new stopping times for the (general) drawdown process, namely, the Parisian drawdown and ultimate drawdown under the exponential implementation delays. We provide quantitative analysis of their distributional properties of interest through the generalized scale functions, whose properties are examined as well. We then discuss their relationships with the existing results on exit times and occupation times as the application of our main results. Another application in the fair market valuation of drawdown insurance is also presented and illustrated in a numerical example.

Suggested Citation

  • Li, Shu & Zhou, Xiaowen, 2022. "The Parisian and ultimate drawdowns of Lévy insurance models," Insurance: Mathematics and Economics, Elsevier, vol. 107(C), pages 140-160.
    • Handle: RePEc:eee:insuma:v:107:y:2022:i:c:p:140-160
    DOI: 10.1016/j.insmatheco.2022.08.004
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    References listed on IDEAS

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    1. Cheung, Eric C.K. & Zhu, Wei, 2023. "Cumulative Parisian ruin in finite and infinite time horizons for a renewal risk process with exponential claims," Insurance: Mathematics and Economics, Elsevier, vol. 111(C), pages 84-101.

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    More about this item

    Keywords

    Parisian drawdown; Ultimate drawdown; Lévy process; Scale functions; Exit identities; Drawdown insurance;
    All these keywords.

    JEL classification:

    • C02 - Mathematical and Quantitative Methods - - General - - - Mathematical Economics
    • G22 - Financial Economics - - Financial Institutions and Services - - - Insurance; Insurance Companies; Actuarial Studies

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