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On the time spent in the red by a refracted L\'evy risk process

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  • Jean-Franc{c}ois Renaud

Abstract

In this paper, we introduce an insurance ruin model with adaptive premium rate, thereafter refered to as restructuring/refraction, in which classical ruin and bankruptcy are distinguished. In this model, the premium rate is increased as soon as the wealth process falls into the red zone and is brought back to its regular level when the process recovers. The analysis is mainly focused on the time a refracted L\'evy risk process spends in the red zone (analogous to the duration of the negative surplus). Building on results from Kyprianou and Loeffen (2010) and Loeffen et al. (2012), we identify the distribution of various functionals related to occupation times of refracted spectrally negative L\'evy processes. For example, these results are used to compute the probability of bankruptcy and the probability of Parisian ruin in this model with restructuring.

Suggested Citation

  • Jean-Franc{c}ois Renaud, 2013. "On the time spent in the red by a refracted L\'evy risk process," Papers 1306.4619, arXiv.org.
    • Handle: RePEc:arx:papers:1306.4619
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    References listed on IDEAS

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    1. Albrecher, Hansjörg & Cheung, Eric C.K. & Thonhauser, Stefan, 2011. "Randomized Observation Periods for the Compound Poisson Risk Model: Dividends," ASTIN Bulletin, Cambridge University Press, vol. 41(2), pages 645-672, November.
    2. 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.
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    Cited by:

    1. Zhou, Jiang & Wu, Lan, 2015. "The time of deducting fees for variable annuities under the state-dependent fee structure," Insurance: Mathematics and Economics, Elsevier, vol. 61(C), pages 125-134.

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