IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v10y2022i4p606-d750923.html
   My bibliography  Save this article

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
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/10/4/606/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/10/4/606/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. 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.
    2. 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.
    3. 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.
    4. Zinoviy Landsman & Emiliano Valdez, 2003. "Tail Conditional Expectations for Elliptical Distributions," North American Actuarial Journal, Taylor & Francis Journals, vol. 7(4), pages 55-71.
    5. 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.
    6. 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.
    7. 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.
    8. Landsman, Zinoviy, 2010. "On the Tail Mean-Variance optimal portfolio selection," Insurance: Mathematics and Economics, Elsevier, vol. 46(3), pages 547-553, June.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    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.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. 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.
    2. Mohammed, Nawaf & Furman, Edward & Su, Jianxi, 2021. "Can a regulatory risk measure induce profit-maximizing risk capital allocations? The case of conditional tail expectation," Insurance: Mathematics and Economics, Elsevier, vol. 101(PB), pages 425-436.
    3. Baishuai Zuo & Chuancun Yin, 2022. "Doubly truncated moment risk measures for elliptical distributions," Papers 2203.01091, arXiv.org.
    4. Baishuai Zuo & Chuancun Yin, 2020. "Conditional tail risk expectations for location-scale mixture of elliptical distributions," Papers 2007.09350, arXiv.org.
    5. Shushi, Tomer, 2019. "The Minkowski length of a spherical random vector," Statistics & Probability Letters, Elsevier, vol. 153(C), pages 104-107.
    6. 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.
    7. Baishuai Zuo & Chuancun Yin & Jing Yao, 2023. "Multivariate range Value-at-Risk and covariance risk measures for elliptical and log-elliptical distributions," Papers 2305.09097, arXiv.org.
    8. Xu, Maochao & Mao, Tiantian, 2013. "Optimal capital allocation based on the Tail Mean–Variance model," Insurance: Mathematics and Economics, Elsevier, vol. 53(3), pages 533-543.
    9. Eini, Esmat Jamshidi & Khaloozadeh, Hamid, 2021. "The tail mean–variance optimal portfolio selection under generalized skew-elliptical distribution," Insurance: Mathematics and Economics, Elsevier, vol. 98(C), pages 44-50.
    10. Owadally, Iqbal & Landsman, Zinoviy, 2013. "A characterization of optimal portfolios under the tail mean–variance criterion," Insurance: Mathematics and Economics, Elsevier, vol. 52(2), pages 213-221.
    11. Wang, Bingjie & Li, Jinzhu, 2024. "Asymptotic results on tail moment for light-tailed risks," Insurance: Mathematics and Economics, Elsevier, vol. 114(C), pages 43-55.
    12. Kim, Joseph H.T. & Kim, So-Yeun, 2019. "Tail risk measures and risk allocation for the class of multivariate normal mean–variance mixture distributions," Insurance: Mathematics and Economics, Elsevier, vol. 86(C), pages 145-157.
    13. Nawaf Mohammed & Edward Furman & Jianxi Su, 2021. "Can a regulatory risk measure induce profit-maximizing risk capital allocations? The case of Conditional Tail Expectation," Papers 2102.05003, arXiv.org, revised Aug 2021.
    14. Haitham M. Yousof & Yusra Tashkandy & Walid Emam & M. Masoom Ali & Mohamed Ibrahim, 2023. "A New Reciprocal Weibull Extension for Modeling Extreme Values with Risk Analysis under Insurance Data," Mathematics, MDPI, vol. 11(4), pages 1-26, February.
    15. Jiang, Chun-Fu & Peng, Hong-Yi & Yang, Yu-Kuan, 2016. "Tail variance of portfolio under generalized Laplace distribution," Applied Mathematics and Computation, Elsevier, vol. 282(C), pages 187-203.
    16. Furman, Edward & Kye, Yisub & Su, Jianxi, 2021. "Multiplicative background risk models: Setting a course for the idiosyncratic risk factors distributed phase-type," Insurance: Mathematics and Economics, Elsevier, vol. 96(C), pages 153-167.
    17. Fouad Marri & Khouzeima Moutanabbir, 2021. "Risk aggregation and capital allocation using a new generalized Archimedean copula," Papers 2103.10989, arXiv.org.
    18. Mohamed Ibrahim & Walid Emam & Yusra Tashkandy & M. Masoom Ali & Haitham M. Yousof, 2023. "Bayesian and Non-Bayesian Risk Analysis and Assessment under Left-Skewed Insurance Data and a Novel Compound Reciprocal Rayleigh Extension," Mathematics, MDPI, vol. 11(7), pages 1-26, March.
    19. Furman, Edward & Wang, Ruodu & Zitikis, Ričardas, 2017. "Gini-type measures of risk and variability: Gini shortfall, capital allocations, and heavy-tailed risks," Journal of Banking & Finance, Elsevier, vol. 83(C), pages 70-84.
    20. Fouad Marri & Khouzeima Moutanabbir, 2021. "Risk aggregation and capital allocation using a new generalized Archimedean copula," Working Papers hal-03169291, HAL.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:gam:jmathe:v:10:y:2022:i:4:p:606-:d:750923. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.