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Stochastic ordering of bivariate elliptical distributions

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  • Landsman, Zinoviy
  • Tsanakas, Andreas

Abstract

It is shown that for elliptically distributed bivariate random vectors, the riskiness and dependence strength of random portfolios, in the sense of the univariate convex and bivariate concordance stochastic orders respectively, can be simply characterised in terms of the vector's [Sigma]-matrix.

Suggested Citation

  • Landsman, Zinoviy & Tsanakas, Andreas, 2006. "Stochastic ordering of bivariate elliptical distributions," Statistics & Probability Letters, Elsevier, vol. 76(5), pages 488-494, March.
    • Handle: RePEc:eee:stapro:v:76:y:2006:i:5:p:488-494
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    References listed on IDEAS

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    1. Ding, Ying & Zhang, Xinsheng, 2004. "Some stochastic orders of Kotz-type distributions," Statistics & Probability Letters, Elsevier, vol. 69(4), pages 389-396, October.
    2. Dhaene, Jan & Goovaerts, Marc J., 1996. "Dependency of Risks and Stop-Loss Order1," ASTIN Bulletin, Cambridge University Press, vol. 26(2), pages 201-212, November.
    3. Fang, Hong-Bin & Fang, Kai-Tai & Kotz, Samuel, 2002. "The Meta-elliptical Distributions with Given Marginals," Journal of Multivariate Analysis, Elsevier, vol. 82(1), pages 1-16, July.
    4. Alfred Müller, 2001. "Stochastic Ordering of Multivariate Normal Distributions," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 53(3), pages 567-575, September.
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    Cited by:

    1. Pellerey, Franco & Laniado Rodas, Henry, 2012. "Portfolio selection through and extremality stochastic order," DES - Working Papers. Statistics and Econometrics. WS ws121812, Universidad Carlos III de Madrid. Departamento de Estadística.
    2. Amiri, Mehdi & Izadkhah, Salman & Jamalizadeh, Ahad, 2020. "Linear orderings of the scale mixtures of the multivariate skew-normal distribution," Journal of Multivariate Analysis, Elsevier, vol. 179(C).
    3. Dhaene, J. & Henrard, L. & Landsman, Z. & Vandendorpe, A. & Vanduffel, S., 2008. "Some results on the CTE-based capital allocation rule," Insurance: Mathematics and Economics, Elsevier, vol. 42(2), pages 855-863, April.
    4. Ansari, Jonathan & Rüschendorf, Ludger, 2021. "Ordering results for elliptical distributions with applications to risk bounds," Journal of Multivariate Analysis, Elsevier, vol. 182(C).
    5. Laniado, Henry & Lillo, Rosa E. & Pellerey, Franco & Romo, Juan, 2012. "Portfolio selection through an extremality stochastic order," Insurance: Mathematics and Economics, Elsevier, vol. 51(1), pages 1-9.
    6. Xu Guo & Andreas Wagener & Wing-Keung Wong & Lixing Zhu, 2018. "The two-moment decision model with additive risks," Risk Management, Palgrave Macmillan, vol. 20(1), pages 77-94, February.
    7. Tsanakas, Andreas, 2008. "Risk measurement in the presence of background risk," Insurance: Mathematics and Economics, Elsevier, vol. 42(2), pages 520-528, April.
    8. Chuancun Yin, 2019. "Stochastic Orderings of Multivariate Elliptical Distributions," Papers 1910.07158, arXiv.org, revised Nov 2019.
    9. Pan, Xiaoqing & Qiu, Guoxin & Hu, Taizhong, 2016. "Stochastic orderings for elliptical random vectors," Journal of Multivariate Analysis, Elsevier, vol. 148(C), pages 83-88.

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