IDEAS home Printed from https://ideas.repec.org/a/eee/insuma/v60y2015icp11-18.html
   My bibliography  Save this article

Asymptotic results for conditional measures of association of a random sum

Author

Listed:
  • Asimit, Alexandru V.
  • Chen, Yiqing

Abstract

Asymptotic results are obtained for several conditional measures of association. The chosen random variables are the first two order statistics and the total sum within a random sum. Many of the results have confirmed the “one-jump” property of the risk model. Non-trivial limits are obtained when the dependence among the first two order statistics is considered. Our results help in understanding the extreme behaviour of well-known reinsurance treaties that involve only few large claims. Interestingly, the Pearson product-moment correlation coefficient between the first two order statistics provides an alternative procedure to estimate the tail index of the underlying distribution.

Suggested Citation

  • Asimit, Alexandru V. & Chen, Yiqing, 2015. "Asymptotic results for conditional measures of association of a random sum," Insurance: Mathematics and Economics, Elsevier, vol. 60(C), pages 11-18.
  • Handle: RePEc:eee:insuma:v:60:y:2015:i:c:p:11-18
    DOI: 10.1016/j.insmatheco.2014.10.012
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0167668714001395
    Download Restriction: Full text for ScienceDirect subscribers only

    File URL: https://libkey.io/10.1016/j.insmatheco.2014.10.012?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Hashorva, Enkelejd, 2007. "On the asymptotic distribution of certain bivariate reinsurance treaties," Insurance: Mathematics and Economics, Elsevier, vol. 40(2), pages 200-208, March.
    2. Jiang, Jun & Tang, Qihe, 2008. "Reinsurance under the LCR and ECOMOR treaties with emphasis on light-tailed claims," Insurance: Mathematics and Economics, Elsevier, vol. 43(3), pages 431-436, December.
    3. Peng, Liang, 2014. "Joint tail of ECOMOR and LCR reinsurance treaties," Insurance: Mathematics and Economics, Elsevier, vol. 58(C), pages 116-120.
    4. Hashorva, Enkelejd & Li, Jinzhu, 2013. "ECOMOR and LCR reinsurance with gamma-like claims," Insurance: Mathematics and Economics, Elsevier, vol. 53(1), pages 206-215.
    5. Hansjörg Albrecher & Christian Y. Robert & Jef L. Teugels, 2014. "Joint Asymptotic Distributions of Smallest and Largest Insurance Claims," Risks, MDPI, vol. 2(3), pages 1-26, July.
    6. Asimit, Alexandru V. & Jones, Bruce L., 2008. "Dependence and the asymptotic behavior of large claims reinsurance," Insurance: Mathematics and Economics, Elsevier, vol. 43(3), pages 407-411, December.
    7. Christian Yann Robert & Hansjörg Albrecher & Jef Teugels, 2014. "Joint Asymptotic Distributions of Smallest and Largest Insurance Claims," Post-Print hal-02006777, HAL.
    8. Tang, Qihe & Yang, Fan, 2012. "On the Haezendonck–Goovaerts risk measure for extreme risks," Insurance: Mathematics and Economics, Elsevier, vol. 50(1), pages 217-227.
    Full references (including those not matched with items on IDEAS)

    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. Peng, Liang, 2014. "Joint tail of ECOMOR and LCR reinsurance treaties," Insurance: Mathematics and Economics, Elsevier, vol. 58(C), pages 116-120.
    2. Søren Asmussen & Jaakko Lehtomaa, 2017. "Distinguishing Log-Concavity from Heavy Tails," Risks, MDPI, vol. 5(1), pages 1-14, February.
    3. Albrecher, Hansjörg & García Flores, Brandon, 2022. "Asymptotic analysis of generalized Greenwood statistics for very heavy tails," Statistics & Probability Letters, Elsevier, vol. 185(C).
    4. Dembińska, Anna & Buraczyńska, Aneta, 2019. "The long-term behavior of number of near-maximum insurance claims," Insurance: Mathematics and Economics, Elsevier, vol. 88(C), pages 226-237.
    5. Hashorva, Enkelejd & Li, Jinzhu, 2013. "ECOMOR and LCR reinsurance with gamma-like claims," Insurance: Mathematics and Economics, Elsevier, vol. 53(1), pages 206-215.
    6. 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.
    7. Guo, Fenglong, 2022. "Ruin probability of a continuous-time model with dependence between insurance and financial risks caused by systematic factors," Applied Mathematics and Computation, Elsevier, vol. 413(C).
    8. Xing-Fang Huang & Ting Zhang & Yang Yang & Tao Jiang, 2017. "Ruin Probabilities in a Dependent Discrete-Time Risk Model With Gamma-Like Tailed Insurance Risks," Risks, MDPI, vol. 5(1), pages 1-14, March.
    9. Liu, Qing & Peng, Liang & Wang, Xing, 2017. "Haezendonck–Goovaerts risk measure with a heavy tailed loss," Insurance: Mathematics and Economics, Elsevier, vol. 76(C), pages 28-47.
    10. Hashorva, Enkelejd & Ling, Chengxiu & Peng, Zuoxiang, 2014. "Second-order tail asymptotics of deflated risks," Insurance: Mathematics and Economics, Elsevier, vol. 56(C), pages 88-101.
    11. Mao, Tiantian & Stupfler, Gilles & Yang, Fan, 2023. "Asymptotic properties of generalized shortfall risk measures for heavy-tailed risks," Insurance: Mathematics and Economics, Elsevier, vol. 111(C), pages 173-192.
    12. Cheung, Ka Chun & Lo, Ambrose, 2013. "General lower bounds on convex functionals of aggregate sums," Insurance: Mathematics and Economics, Elsevier, vol. 53(3), pages 884-896.
    13. Wei, Li & Yuan, Zhongyi, 2016. "The loss given default of a low-default portfolio with weak contagion," Insurance: Mathematics and Economics, Elsevier, vol. 66(C), pages 113-123.
    14. Claudia Kluppelberg & Miriam Isabel Seifert, 2016. "Conditional loss probabilities for systems of economic agents sharing light-tailed claims with analysis of portfolio diversification benefits," Papers 1612.07132, arXiv.org.
    15. Tadese, Mekonnen & Drapeau, Samuel, 2020. "Relative bound and asymptotic comparison of expectile with respect to expected shortfall," Insurance: Mathematics and Economics, Elsevier, vol. 93(C), pages 387-399.
    16. Braun, Alexander & Ben Ammar, Semir & Eling, Martin, 2019. "Asset pricing and extreme event risk: Common factors in ILS fund returns," Journal of Banking & Finance, Elsevier, vol. 102(C), pages 59-78.
    17. Jiang, Jun & Tang, Qihe, 2008. "Reinsurance under the LCR and ECOMOR treaties with emphasis on light-tailed claims," Insurance: Mathematics and Economics, Elsevier, vol. 43(3), pages 431-436, December.
    18. Tang, Qihe & Yang, Fan, 2014. "Extreme value analysis of the Haezendonck–Goovaerts risk measure with a general Young function," Insurance: Mathematics and Economics, Elsevier, vol. 59(C), pages 311-320.
    19. Leipus, Remigijus & Paukštys, Saulius & Šiaulys, Jonas, 2021. "Tails of higher-order moments of sums with heavy-tailed increments and application to the Haezendonck–Goovaerts risk measure," Statistics & Probability Letters, Elsevier, vol. 170(C).
    20. Wang, Xing & Peng, Liang, 2016. "Inference for intermediate Haezendonck–Goovaerts risk measure," Insurance: Mathematics and Economics, Elsevier, vol. 68(C), pages 231-240.

    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:eee:insuma:v:60:y:2015:i:c:p:11-18. 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: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/locate/inca/505554 .

    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.