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

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  • Sordo, Miguel A.
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    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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    Bibliographic Info

    Article provided by Elsevier in its journal Insurance: Mathematics and Economics.

    Volume (Year): 45 (2009)
    Issue (Month): 3 (December)
    Pages: 466-469

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    Handle: RePEc:eee:insuma:v:45:y:2009:i:3:p:466-469

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    Web page: http://www.elsevier.com/locate/inca/505554

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    Keywords: Excess wealth order Dispersive order Conditional tail variance Classes of risk measures;

    References

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    1. Ramos, Héctor M. & Sordo, Miguel A., 2003. "Dispersion measures and dispersive orderings," Statistics & Probability Letters, Elsevier, vol. 61(2), pages 123-131, January.
    2. Chateauneuf, Alain & Cohen, Michele & Meilijson, Isaac, 2004. "Four notions of mean-preserving increase in risk, risk attitudes and applications to the rank-dependent expected utility model," Journal of Mathematical Economics, Elsevier, vol. 40(5), pages 547-571, August.
    3. Rojo, Javier & He, Guo Zhong, 1991. "New properties and characterizations of the dispersive ordering," Statistics & Probability Letters, Elsevier, vol. 11(4), pages 365-372, April.
    4. Furman, Edward & Zitikis, Ricardas, 2008. "Weighted premium calculation principles," Insurance: Mathematics and Economics, Elsevier, vol. 42(1), pages 459-465, February.
    5. Sordo, Miguel A., 2009. "On the relationship of location-independent riskier order to the usual stochastic order," Statistics & Probability Letters, Elsevier, vol. 79(2), pages 155-157, January.
    6. Newbery, David, 1970. "A theorem on the measurement of inequality," Journal of Economic Theory, Elsevier, vol. 2(3), pages 264-266, September.
    7. Hu, Taizhong & Chen, Jing & Yao, Junchao, 2006. "Preservation of the location independent risk order under convolution," Insurance: Mathematics and Economics, Elsevier, vol. 38(2), pages 406-412, April.
    8. 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.
    9. Carole Bernard & Weidong Tian, 2009. "Optimal Reinsurance Arrangements Under Tail Risk Measures," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 76(3), pages 709-725.
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    Cited by:
    1. 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.
    2. 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.

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