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Finite time Parisian ruin of an integrated Gaussian risk model

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  • Peng, Xiaofan
  • Luo, Li

Abstract

In this paper we investigate the finite time Parisian ruin probability for an integrated Gaussian risk process. Under certain assumptions, we find that the Parisian ruin probability and the classical ruin probability are on the log-scale asymptotically the same. Moreover, if the time length required by the Parisian ruin tends to zero as the initial reserve goes to infinity, the Parisian ruin probability and the classical one are the same also in the precise asymptotic behavior. Furthermore, we derive an approximation for the scaled conditional ruin time.

Suggested Citation

  • Peng, Xiaofan & Luo, Li, 2017. "Finite time Parisian ruin of an integrated Gaussian risk model," Statistics & Probability Letters, Elsevier, vol. 124(C), pages 22-29.
    • Handle: RePEc:eee:stapro:v:124:y:2017:i:c:p:22-29
    DOI: 10.1016/j.spl.2016.12.019
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    References listed on IDEAS

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    1. Ronnie Loeffen & Irmina Czarna & Zbigniew Palmowski, 2011. "Parisian ruin probability for spectrally negative L\'{e}vy processes," Papers 1102.4055, arXiv.org, revised Mar 2013.
    2. Bai, Long & Luo, Li, 2017. "Parisian ruin of the Brownian motion risk model with constant force of interest," Statistics & Probability Letters, Elsevier, vol. 120(C), pages 34-44.
    3. Dassios, Angelos & Wu, Shanle, 2008. "Parisian ruin with exponential claims," LSE Research Online Documents on Economics 32033, London School of Economics and Political Science, LSE Library.
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