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Tail Conditional Moments for Location-Scale Mixture of Elliptical Distributions

Author

Listed:
  • Xiangyu Han

    (School of Statistics and Data Science, Qufu Normal University, Qufu 273165, China)

  • Chuancun Yin

    (School of Statistics and Data Science, Qufu Normal University, Qufu 273165, China)

Abstract

We present the general results on the univariate tail conditional moments for a location-scale mixture of elliptical distributions. Examples include the location-scale mixture of normal, location-scale mixture of Student’s t , location-scale mixture of logistic, and location-scale mixture of Laplace distributions. More specifically, we give the tail variance, the tail conditional skewness, and the tail conditional kurtosis of generalised hyperbolic distribution and Student–GIG mixture distribution. We give an illustrative example, which discusses the TCE, TV, TCS and TCK of three stocks, including Amazon, Google and Apple.

Suggested Citation

  • Xiangyu Han & Chuancun Yin, 2022. "Tail Conditional Moments for Location-Scale Mixture of Elliptical Distributions," Mathematics, MDPI, vol. 10(4), pages 1-21, February.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:4:p:606-:d:750923
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    References listed on IDEAS

    as
    1. Zinoviy Landsman & Emiliano Valdez, 2003. "Tail Conditional Expectations for Elliptical Distributions," North American Actuarial Journal, Taylor & Francis Journals, vol. 7(4), pages 55-71.
    2. Ignatieva, Katja & Landsman, Zinoviy, 2019. "Conditional tail risk measures for the skewed generalised hyperbolic family," Insurance: Mathematics and Economics, Elsevier, vol. 86(C), pages 98-114.
    3. 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.
    4. Joseph Kim, 2010. "Conditional Tail Moments of the Exponential Family and Its Related Distributions," North American Actuarial Journal, Taylor & Francis Journals, vol. 14(2), pages 198-216.
    5. Esmat Jamshidi Eini & Hamid Khaloozadeh, 2021. "Tail conditional moment for generalized skew-elliptical distributions," Journal of Applied Statistics, Taylor & Francis Journals, vol. 48(13-15), pages 2285-2305, November.
    6. Landsman, Zinoviy, 2010. "On the Tail Mean-Variance optimal portfolio selection," Insurance: Mathematics and Economics, Elsevier, vol. 46(3), pages 547-553, June.
    7. Xiang Deng & Jing Yao, 2018. "On the property of multivariate generalized hyperbolic distribution and the Stein-type inequality," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 47(21), pages 5346-5356, November.
    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.
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    Cited by:

    1. Roman V. Ivanov, 2023. "The Semi-Hyperbolic Distribution and Its Applications," Stats, MDPI, vol. 6(4), pages 1-21, October.
    2. Xiao Jiang & Saralees Nadarajah & Thomas Hitchen, 2024. "A Review of Generalized Hyperbolic Distributions," Computational Economics, Springer;Society for Computational Economics, vol. 64(1), pages 595-624, July.

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