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Comparison of risks based on the expected proportional shortfall

Author

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  • Belzunce, Félix
  • Pinar, José F.
  • Ruiz, José M.
  • Sordo, Miguel A.

Abstract

In this paper, we consider a new criterion to compare risks based on the notion of expected proportional shortfall. This criterion is useful for comparing risks of different nature and does not depend on the base currency. We study its relationships with other criteria and provide some characterizations that highlight the role of this new criterion in the context of comparisons of risks.

Suggested Citation

  • Belzunce, Félix & Pinar, José F. & Ruiz, José M. & Sordo, Miguel A., 2012. "Comparison of risks based on the expected proportional shortfall," Insurance: Mathematics and Economics, Elsevier, vol. 51(2), pages 292-302.
    • Handle: RePEc:eee:insuma:v:51:y:2012:i:2:p:292-302
    DOI: 10.1016/j.insmatheco.2012.05.003
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    References listed on IDEAS

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    1. Miguel Sordo & Héctor Ramos, 2007. "Characterization of stochastic orders by L-functionals," Statistical Papers, Springer, vol. 48(2), pages 249-263, April.
    2. Yaari, Menahem E, 1987. "The Dual Theory of Choice under Risk," Econometrica, Econometric Society, vol. 55(1), pages 95-115, January.
    3. Agostino Tarsitano, 2004. "A new class of inequality measures based on a ratio of L-statistics," Metron - International Journal of Statistics, Dipartimento di Statistica, Probabilità e Statistiche Applicate - University of Rome, vol. 0(1), pages 137-160.
    4. Shaun Wang, 1998. "An Actuarial Index of the Right-Tail Risk," North American Actuarial Journal, Taylor & Francis Journals, vol. 2(2), pages 88-101.
    5. Sordo, Miguel A. & Suárez-Llorens, Alfonso, 2011. "Stochastic comparisons of distorted variability measures," Insurance: Mathematics and Economics, Elsevier, vol. 49(1), pages 11-17, July.
    6. Bruce Jones & Ričardas Zitikis, 2003. "Empirical Estimation of Risk Measures and Related Quantities," North American Actuarial Journal, Taylor & Francis Journals, vol. 7(4), pages 44-54.
    7. Wang, Shaun S. & Young, Virginia R., 1998. "Ordering risks: Expected utility theory versus Yaari's dual theory of risk," Insurance: Mathematics and Economics, Elsevier, vol. 22(2), pages 145-161, June.
    8. Jones, Bruce L. & Zitikis, Ricardas, 2007. "Risk measures, distortion parameters, and their empirical estimation," Insurance: Mathematics and Economics, Elsevier, vol. 41(2), pages 279-297, September.
    9. Sordo, Miguel A., 2009. "Comparing tail variabilities of risks by means of the excess wealth order," Insurance: Mathematics and Economics, Elsevier, vol. 45(3), pages 466-469, December.
    10. Sordo, Miguel A., 2008. "Characterizations of classes of risk measures by dispersive orders," Insurance: Mathematics and Economics, Elsevier, vol. 42(3), pages 1028-1034, June.
    Full references (including those not matched with items on IDEAS)

    Citations

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    Cited by:

    1. Antonio Arriaza & Félix Belzunce & Carolina Martínez-Riquelme, 2021. "Sufficient Conditions for some Transform Orders Based on the Quantile Density Ratio," Methodology and Computing in Applied Probability, Springer, vol. 23(1), pages 29-52, March.
    2. Masato Okamoto, 2022. "Lorenz and Polarization Orderings of the Double-Pareto Lognormal Distribution and Other Size Distributions," Sankhya B: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 84(2), pages 548-574, November.
    3. Félix Belzunce & Carolina Martínez-Riquelme & José M. Ruiz & Miguel A. Sordo, 2017. "On the Comparison of Relative Spacings with Applications," Methodology and Computing in Applied Probability, Springer, vol. 19(2), pages 357-376, June.
    4. Marcelo Brutti Righi & Paulo Sergio Ceretta, 2015. "Shortfall Deviation Risk: An alternative to risk measurement," Papers 1501.02007, arXiv.org, revised May 2016.
    5. Aigner, Maximilian & Chavez-Demoulin, Valérie & Guillou, Armelle, 2022. "Measuring and comparing risks of different types," Insurance: Mathematics and Economics, Elsevier, vol. 102(C), pages 1-21.
    6. Stephen Chan & Saralees Nadarajah, 2019. "Risk: An R Package for Financial Risk Measures," Computational Economics, Springer;Society for Computational Economics, vol. 53(4), pages 1337-1351, April.
    7. Antonia Castaño-Martínez & Gema Pigueiras & Miguel A. Sordo, 2021. "On the Increasing Convex Order of Relative Spacings of Order Statistics," Mathematics, MDPI, vol. 9(6), pages 1-12, March.
    8. Belzunce, Félix & Pinar, José F. & Ruiz, José M. & Sordo, Miguel A., 2013. "Comparison of concentration for several families of income distributions," Statistics & Probability Letters, Elsevier, vol. 83(4), pages 1036-1045.

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    More about this item

    Keywords

    Risk measures; Comparison of risks; Expected shortfall;
    All these keywords.

    JEL classification:

    • G32 - Financial Economics - - Corporate Finance and Governance - - - Financing Policy; Financial Risk and Risk Management; Capital and Ownership Structure; Value of Firms; Goodwill

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