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Tail conditional moments for elliptical and log-elliptical distributions

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  • Landsman, Zinoviy
  • Makov, Udi
  • Shushi, Tomer

Abstract

In this paper we provide the tail conditional moments for the class of elliptical distributions, which was introduced in Kelker (1970) and was widely discussed in Gupta et al. (2013) and for the class of log-elliptical distributions. These families of distributions include some important members such as the normal, Student-t, logistic, Laplace, and log-normal distributions. We give analytic formulae for the nth higher order unconditional moments of elliptical distributions, which has not been provided before. We also propose novel risk measures, the tail conditional skewness and the tail conditional kurtosis, for examining the skewness and the kurtosis of the tail of loss distributions, respectively.

Suggested Citation

  • Landsman, Zinoviy & Makov, Udi & Shushi, Tomer, 2016. "Tail conditional moments for elliptical and log-elliptical distributions," Insurance: Mathematics and Economics, Elsevier, vol. 71(C), pages 179-188.
  • Handle: RePEc:eee:insuma:v:71:y:2016:i:c:p:179-188
    DOI: 10.1016/j.insmatheco.2016.09.001
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    References listed on IDEAS

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    2. Landsman, Zinoviy & Pat, Nika & Dhaene, Jan, 2013. "Tail Variance premiums for log-elliptical distributions," Insurance: Mathematics and Economics, Elsevier, vol. 52(3), pages 441-447.
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    7. Landsman, Zinoviy, 2010. "On the Tail Mean-Variance optimal portfolio selection," Insurance: Mathematics and Economics, Elsevier, vol. 46(3), pages 547-553, June.
    8. Furman, Edward & Landsman, Zinoviy, 2006. "Tail Variance Premium with Applications for Elliptical Portfolio of Risks," ASTIN Bulletin, Cambridge University Press, vol. 36(2), pages 433-462, November.
    9. Furman, Edward & Landsman, Zinoviy, 2005. "Risk capital decomposition for a multivariate dependent gamma portfolio," Insurance: Mathematics and Economics, Elsevier, vol. 37(3), pages 635-649, December.
    10. Yang, Yang & Ignatavičiūtė, Eglė & Šiaulys, Jonas, 2015. "Conditional tail expectation of randomly weighted sums with heavy-tailed distributions," Statistics & Probability Letters, Elsevier, vol. 105(C), pages 20-28.
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    Cited by:

    1. Nicole Bauerle & Tomer Shushi, 2019. "Risk Management with Tail Quasi-Linear Means," Papers 1902.06941, arXiv.org, revised Jan 2020.
    2. Shushi, Tomer, 2019. "A note on the coefficients of elliptical random variables," Statistics & Probability Letters, Elsevier, vol. 152(C), pages 153-155.
    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. Bhati, Deepesh & Ravi, Sreenivasan, 2018. "On generalized log-Moyal distribution: A new heavy tailed size distribution," Insurance: Mathematics and Economics, Elsevier, vol. 79(C), pages 247-259.
    5. Shushi, Tomer, 2019. "The Minkowski length of a spherical random vector," Statistics & Probability Letters, Elsevier, vol. 153(C), pages 104-107.

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