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Comparison results of range-based quantities in the classical risk models

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  • Lkabous, Mohamed Amine
  • Yang, Mengni

Abstract

In this paper, we investigate the range-based risk quantities in classical risk models. Specifically, we present some comparison results with respect to the stochastic ordering. We also propose some range-based VaR-type risk measures and study their properties, providing insights into their practical applications and implications for risk management.

Suggested Citation

  • Lkabous, Mohamed Amine & Yang, Mengni, 2025. "Comparison results of range-based quantities in the classical risk models," Statistics & Probability Letters, Elsevier, vol. 223(C).
    • Handle: RePEc:eee:stapro:v:223:y:2025:i:c:s0167715225000732
    DOI: 10.1016/j.spl.2025.110428
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    References listed on IDEAS

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    1. Bartoszewicz, Jaroslaw, 1986. "Dispersive ordering and the total time on test transformation," Statistics & Probability Letters, Elsevier, vol. 4(6), pages 285-288, October.
    2. Picard, Philippe, 1994. "On some measures of the severity of ruin in the classical Poisson model," Insurance: Mathematics and Economics, Elsevier, vol. 14(2), pages 107-115, May.
    3. 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.
    4. Bartoszewicz, J., 1987. "A note on dispersive ordering defined by hazard functions," Statistics & Probability Letters, Elsevier, vol. 6(1), pages 13-16, September.
    5. Li, Xin & Liu, Haibo & Tang, Qihe & Zhu, Jinxia, 2020. "Liquidation risk in insurance under contemporary regulatory frameworks," Insurance: Mathematics and Economics, Elsevier, vol. 93(C), pages 36-49.
    6. 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.
    7. Trufin, Julien & Albrecher, Hansjoerg & Denuit, Michel, 2011. "Properties of risk measures derived from ruin theory," LIDAM Reprints ISBA 2011019, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    8. 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.
    9. Ilie-Radu Mitric & Julien Trufin, 2016. "On a risk measure inspired from the ruin probability and the expected deficit at ruin," Scandinavian Actuarial Journal, Taylor & Francis Journals, vol. 2016(10), pages 932-951, November.
    10. Bin Li & Qihe Tang & Lihe Wang & Xiaowen Zhou, 2014. "Liquidation risk in the presence of Chapters 7 and 11 of the US bankruptcy code," Journal of Financial Engineering (JFE), World Scientific Publishing Co. Pte. Ltd., vol. 1(03), pages 1-19.
    11. 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.
    12. Etienne Tanré & Pierre Vallois, 2006. "Range of Brownian Motion with Drift," Journal of Theoretical Probability, Springer, vol. 19(1), pages 45-69, January.
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