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Properties of a Risk Measure Derived from Ruin Theory

Author

Listed:
  • Julien Trufin

    (Institut de Statistique, Biostatistique et Sciences Actuarielles (ISBA), Universite Catholique de Louvain, B-1348 Louvain-la-Neuve, Belgium)

  • Hansjoerg Albrecher

    (Ecole des HEC (Business School), University of Lausanne, Lausanne CH-1015, Switzerland)

  • Michel M Denuit

    (Institut de Statistique, Biostatistique et Sciences Actuarielles (ISBA), Universite Catholique de Louvain, B-1348 Louvain-la-Neuve, Belgium)

Abstract

This paper studies a risk measure inherited from ruin theory and investigates some of its properties. Specifically, we consider a value-at-risk (VaR)-type risk measure defined as the smallest initial capital needed to ensure that the ultimate ruin probability is less than a given level. This VaR-type risk measure turns out to be equivalent to the VaR of the maximal deficit of the ruin process in infinite time. A related Tail-VaR-type risk measure is also discussed.

Suggested Citation

  • 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.
    • Handle: RePEc:pal:genrir:v:36:y:2011:i:2:p:174-188
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    Citations

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    Cited by:

    1. 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.
    2. repec:hal:wpaper:hal-00870224 is not listed on IDEAS
    3. 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.
    4. Yue He & Reiichiro Kawai & Yasutaka Shimizu & Kazutoshi Yamazaki, 2022. "The Gerber-Shiu discounted penalty function: A review from practical perspectives," Papers 2203.10680, arXiv.org, revised Dec 2022.
    5. Hirbod Assa & Manuel Morales & Hassan Omidi Firouzi, 2016. "On the Capital Allocation Problem for a New Coherent Risk Measure in Collective Risk Theory," Risks, MDPI, vol. 4(3), pages 1-20, August.
    6. 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.
    7. He, Yue & Kawai, Reiichiro & Shimizu, Yasutaka & Yamazaki, Kazutoshi, 2023. "The Gerber-Shiu discounted penalty function: A review from practical perspectives," Insurance: Mathematics and Economics, Elsevier, vol. 109(C), pages 1-28.
    8. Ragnar Levy Gudmundarson & Manuel Guerra & Alexandra Bugalho de Moura, 2021. "Minimizing ruin probability under dependencies for insurance pricing," Papers 2108.10075, arXiv.org.
    9. Başak Bulut Karageyik & Şule Şahin, 2017. "Determination of the Optimal Retention Level Based on Different Measures," JRFM, MDPI, vol. 10(1), pages 1-21, January.
    10. R.L. Gudmundarson & M. Guerra & A. B. de Moura, 2021. "Minimizing Ruin Probability Under Dependencies for Insurance Pricing," Working Papers REM 2021/0193, ISEG - Lisbon School of Economics and Management, REM, Universidade de Lisboa.
    11. Cossette, Hélène & Marceau, Etienne & Trufin, Julien & Zuyderhoff, Pierre, 2020. "Ruin-based risk measures in discrete-time risk models," Insurance: Mathematics and Economics, Elsevier, vol. 93(C), pages 246-261.
    12. 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.
    13. Guérin, Hélène & Renaud, Jean-François, 2017. "On the distribution of cumulative Parisian ruin," Insurance: Mathematics and Economics, Elsevier, vol. 73(C), pages 116-123.
    14. Yasutaka Shimizu & Zhimin Zhang, 2019. "Asymptotically Normal Estimators of the Ruin Probability for Lévy Insurance Surplus from Discrete Samples," Risks, MDPI, vol. 7(2), pages 1-22, April.
    15. Başak Bulut Karageyik & Şule Şahin, 2016. "Optimal Retention Level for Infinite Time Horizons under MADM," Risks, MDPI, vol. 5(1), pages 1-24, December.

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