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Stochastic ordering of Gini indexes for multivariate elliptical random variables

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  • Chuancun Yin

Abstract

In this paper, we establish the stochastic ordering of the Gini indexes for multivariate elliptical risks which generalized the corresponding results for multivariate normal risks. It is shown that several conditions on dispersion matrices and the components of dispersion matrices of multivariate normal risks for the monotonicity of the Gini index in the usual stochastic order proposed by Samanthi, Wei and Brazauskas (2016) and Kim and Kim (2019) are also suitable for multivariate elliptical risks. We also study the tail probability of Gini index for multivariate elliptical risks and revised a large deviation result for the Gini indexes of multivariate normal risks in Kim and Kim (2019).

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  • Chuancun Yin, 2019. "Stochastic ordering of Gini indexes for multivariate elliptical random variables," Papers 1908.01943, arXiv.org, revised Sep 2019.
    • Handle: RePEc:arx:papers:1908.01943
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    References listed on IDEAS

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    1. Mahmoud Hamada & Emiliano A. Valdez, 2008. "CAPM and Option Pricing With Elliptically Contoured Distributions," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 75(2), pages 387-409, June.
    2. Zinoviy Landsman & Emiliano Valdez, 2003. "Tail Conditional Expectations for Elliptical Distributions," North American Actuarial Journal, Taylor & Francis Journals, vol. 7(4), pages 55-71.
    3. Landsman, Zinoviy & Makov, Udi & Shushi, Tomer, 2018. "A multivariate tail covariance measure for elliptical distributions," Insurance: Mathematics and Economics, Elsevier, vol. 81(C), pages 27-35.
    4. Edward W. (Jed) Frees & Glenn Meyers & A. David Cummings, 2014. "Insurance Ratemaking and a Gini Index," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 81(2), pages 335-366, June.
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    6. Cambanis, Stamatis & Huang, Steel & Simons, Gordon, 1981. "On the theory of elliptically contoured distributions," Journal of Multivariate Analysis, Elsevier, vol. 11(3), pages 368-385, September.
    7. Samanthi, Ranadeera Gamage Madhuka & Wei, Wei & Brazauskas, Vytaras, 2016. "Ordering Gini indexes of multivariate elliptical risks," Insurance: Mathematics and Economics, Elsevier, vol. 68(C), pages 84-91.
    8. Samanthi, Ranadeera G.M. & Wei, Wei & Brazauskas, Vytaras, 2017. "Comparing the riskiness of dependent portfolios via nested L-statistics," Annals of Actuarial Science, Cambridge University Press, vol. 11(2), pages 237-252, September.
    9. Owen, Joel & Rabinovitch, Ramon, 1983. "On the Class of Elliptical Distributions and Their Applications to the Theory of Portfolio Choice," Journal of Finance, American Finance Association, vol. 38(3), pages 745-752, June.
    10. Kim, Bara & Kim, Jeongsim, 2019. "Stochastic ordering of Gini indexes for multivariate elliptical risks," Insurance: Mathematics and Economics, Elsevier, vol. 88(C), pages 151-158.
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    Cited by:

    1. Steven Pav, 2019. "A post hoc test on the Sharpe ratio," Papers 1911.04090, arXiv.org.
    2. Ansari, Jonathan & Rüschendorf, Ludger, 2021. "Ordering results for elliptical distributions with applications to risk bounds," Journal of Multivariate Analysis, Elsevier, vol. 182(C).

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