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A VaR-Type Risk Measure Derived from Cumulative Parisian Ruin for the Classical Risk Model

Author

Listed:
  • Mohamed Amine Lkabous

    (Département de mathématiques, Université du Québec à Montréal (UQAM), Montréal, QC H2X 3Y7, Canada
    These authors contributed equally to this work.)

  • Jean-François Renaud

    (Département de mathématiques, Université du Québec à Montréal (UQAM), Montréal, QC H2X 3Y7, Canada
    These authors contributed equally to this work.)

Abstract

In this short paper, we study a VaR-type risk measure introduced by Guérin and Renaud and which is based on cumulative Parisian ruin. We derive some properties of this risk measure and we compare it to the risk measures of Trufin et al. and Loisel and Trufin.

Suggested Citation

  • Mohamed Amine Lkabous & Jean-François Renaud, 2018. "A VaR-Type Risk Measure Derived from Cumulative Parisian Ruin for the Classical Risk Model," Risks, MDPI, vol. 6(3), pages 1-11, August.
    • Handle: RePEc:gam:jrisks:v:6:y:2018:i:3:p:85-:d:165493
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    References listed on IDEAS

    as
    1. Stéphane Loisel, 2005. "Differentiation of some functionals of risk processes and optimal reserve allocation," Post-Print hal-00397289, HAL.
    2. Loisel, Stéphane & Trufin, Julien, 2014. "Properties of a risk measure derived from the expected area in red," Insurance: Mathematics and Economics, Elsevier, vol. 55(C), pages 191-199.
    3. Stéphane Loisel, 2005. "Differentiation of functionals of risk processes and optimal reserve allocation," Post-Print hal-00397290, HAL.
    4. Lefèvre, Claude & Trufin, Julien & Zuyderhoff, Pierre, 2017. "Some comparison results for finite-time ruin probabilities in the classical risk model," Insurance: Mathematics and Economics, Elsevier, vol. 77(C), pages 143-149.
    5. Beekman, John A., 1985. "A series for infinite time ruin probabilities," Insurance: Mathematics and Economics, Elsevier, vol. 4(2), pages 129-134, April.
    6. Rob Kaas & Marc Goovaerts & Jan Dhaene & Michel Denuit, 2008. "Modern Actuarial Risk Theory," Springer Books, Springer, edition 2, number 978-3-540-70998-5, September.
    7. Stéphane Loisel, 2005. "Differentiation of some functionals of risk processes," Post-Print hal-00157739, HAL.
    8. Stéphane Loisel, 2005. "Differentiation of some functionals of multidimensional risk processes and determination of optimal reserve allocation," Post-Print hal-00397287, HAL.
    9. Guérin, Hélène & Renaud, Jean-François, 2017. "On the distribution of cumulative Parisian ruin," Insurance: Mathematics and Economics, Elsevier, vol. 73(C), pages 116-123.
    10. Julien Trufin & Hansjoerg Albrecher & Michel M Denuit, 2011. "Properties of a Risk Measure Derived from Ruin Theory," The Geneva Risk and Insurance Review, Palgrave Macmillan;International Association for the Study of Insurance Economics (The Geneva Association), vol. 36(2), pages 174-188, December.
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    Citations

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    Cited by:

    1. Lkabous, Mohamed Amine, 2019. "A note on Parisian ruin under a hybrid observation scheme," Statistics & Probability Letters, Elsevier, vol. 145(C), pages 147-157.
    2. David Landriault & Bin Li & Mohamed Amine Lkabous, 2019. "On occupation times in the red of L\'evy risk models," Papers 1903.03721, arXiv.org, revised Jul 2019.
    3. Mohamed Amine Lkabous, 2019. "A note on Parisian ruin under a hybrid observation scheme," Papers 1907.09993, arXiv.org.
    4. 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.
    5. Jiandong Ren & Kristina Sendova & Ričardas Zitikis, 2019. "Special Issue “Risk, Ruin and Survival: Decision Making in Insurance and Finance”," Risks, MDPI, vol. 7(3), pages 1-7, September.

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