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Comparing tail variabilities of risks by means of the excess wealth order

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  • Sordo, Miguel A.

Abstract

There is a growing interest in the actuarial community in employing certain tail conditional characteristics as measures of risk, which are informative about the variability of the losses beyond the value-at-risk (one example is the tail conditional variance, introduced by Furman and Landsman (2006a, 2006b)). However, comparisons of tail risks based on different measures may not always be consistent. In addition, conclusions based on these conditional characteristics depend on the choice of the tail probability p, so different p's also may produce contradictory conclusions. In this note, we suggest comparing tail variabilities of risks by means of the excess wealth order, which makes judgments only if large classes of tail conditional characteristics imply the same conclusion, independently of the choice of p.

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  • 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.
    • Handle: RePEc:eee:insuma:v:45:y:2009:i:3:p:466-469
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    Cited by:

    1. 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.
    2. Nozer Singpurwalla & Anna Gordon, 2014. "Auditing Shaked and Shanthikumar’s ‘excess wealth’," Annals of Operations Research, Springer, vol. 212(1), pages 3-19, January.
    3. Sordo, Miguel A. & Suárez-Llorens, Alfonso & Bello, Alfonso J., 2015. "Comparison of conditional distributions in portfolios of dependent risks," Insurance: Mathematics and Economics, Elsevier, vol. 61(C), pages 62-69.
    4. Gabriella Dellino & Jack P. C. Kleijnen & Carlo Meloni, 2012. "Robust Optimization in Simulation: Taguchi and Krige Combined," INFORMS Journal on Computing, INFORMS, vol. 24(3), pages 471-484, August.
    5. 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.
    6. Jiang, Chun-Fu & Peng, Hong-Yi & Yang, Yu-Kuan, 2016. "Tail variance of portfolio under generalized Laplace distribution," Applied Mathematics and Computation, Elsevier, vol. 282(C), pages 187-203.
    7. Markus Huggenberger & Peter Albrecht, 2022. "Risk pooling and solvency regulation: A policyholder's perspective," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 89(4), pages 907-950, December.
    8. Patricia Ortega-Jiménez & Miguel A. Sordo & Alfonso Suárez-Llorens, 2021. "Stochastic Comparisons of Some Distances between Random Variables," Mathematics, MDPI, vol. 9(9), pages 1-14, April.
    9. Belzunce, Félix & Suárez-Llorens, Alfonso & Sordo, Miguel A., 2012. "Comparison of increasing directionally convex transformations of random vectors with a common copula," Insurance: Mathematics and Economics, Elsevier, vol. 50(3), pages 385-390.
    10. Sun, Hongfang & Chen, Yu & Hu, Taizhong, 2022. "Statistical inference for tail-based cumulative residual entropy," Insurance: Mathematics and Economics, Elsevier, vol. 103(C), pages 66-95.
    11. Sordo, M.A. & Bello, A.J. & Suárez-Llorens, A., 2018. "Stochastic orders and co-risk measures under positive dependence," Insurance: Mathematics and Economics, Elsevier, vol. 78(C), pages 105-113.
    12. Psarrakos, Georgios & Sordo, Miguel A., 2019. "On a family of risk measures based on proportional hazards models and tail probabilities," Insurance: Mathematics and Economics, Elsevier, vol. 86(C), pages 232-240.

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