IDEAS home Printed from https://ideas.repec.org/a/eee/stapro/v52y2001i1p91-100.html
   My bibliography  Save this article

Large deviations for heavy-tailed random sums in compound renewal model

Author

Listed:
  • Tang, Qihe
  • Su, Chun
  • Jiang, Tao
  • Zhang, Jinsong

Abstract

In the present paper we investigate the precise large deviations for heavy-tailed random sums. First, we obtain a result which improves the relative result in Klüppelberg and Mikosch (J. Appl. Probab. 34 (1997) 293). Then we introduce a more realistic risk model than classical ones, named the compound renewal model, and establish the precise large deviations in this model.

Suggested Citation

  • Tang, Qihe & Su, Chun & Jiang, Tao & Zhang, Jinsong, 2001. "Large deviations for heavy-tailed random sums in compound renewal model," Statistics & Probability Letters, Elsevier, vol. 52(1), pages 91-100, March.
  • Handle: RePEc:eee:stapro:v:52:y:2001:i:1:p:91-100
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0167-7152(00)00231-5
    Download Restriction: Full text for ScienceDirect subscribers only

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

    Citations

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


    Cited by:

    1. He, Wei & Cheng, Dongya & Wang, Yuebao, 2013. "Asymptotic lower bounds of precise large deviations with nonnegative and dependent random variables," Statistics & Probability Letters, Elsevier, vol. 83(1), pages 331-338.
    2. Shen, Xinmei & Xu, Menghao & Mills, Ebenezer Fiifi Emire Atta, 2016. "Precise large deviation results for sums of sub-exponential claims in a size-dependent renewal risk model," Statistics & Probability Letters, Elsevier, vol. 114(C), pages 6-13.
    3. Bernackaitė, Emilija & Šiaulys, Jonas, 2015. "The exponential moment tail of inhomogeneous renewal process," Statistics & Probability Letters, Elsevier, vol. 97(C), pages 9-15.
    4. Baltrunas, Aleksandras & Leipus, Remigijus & Siaulys, Jonas, 2008. "Precise large deviation results for the total claim amount under subexponential claim sizes," Statistics & Probability Letters, Elsevier, vol. 78(10), pages 1206-1214, August.
    5. Chen, Yu & Zhang, Weiping, 2007. "Large deviations for random sums of negatively dependent random variables with consistently varying tails," Statistics & Probability Letters, Elsevier, vol. 77(5), pages 530-538, March.
    6. Konstantinides, Dimitrios & Tang, Qihe & Tsitsiashvili, Gurami, 2002. "Estimates for the ruin probability in the classical risk model with constant interest force in the presence of heavy tails," Insurance: Mathematics and Economics, Elsevier, vol. 31(3), pages 447-460, December.
    7. Chen, Yiqing & Yuen, Kam C., 2012. "Precise large deviations of aggregate claims in a size-dependent renewal risk model," Insurance: Mathematics and Economics, Elsevier, vol. 51(2), pages 457-461.
    8. Jiang, Tao & Cui, Sheng & Ming, Ruixing, 2015. "Large deviations for the stochastic present value of aggregate claims in the renewal risk model," Statistics & Probability Letters, Elsevier, vol. 101(C), pages 83-91.
    9. Liu, Li, 2009. "Precise large deviations for dependent random variables with heavy tails," Statistics & Probability Letters, Elsevier, vol. 79(9), pages 1290-1298, May.
    10. Lu, Dawei, 2012. "Lower bounds of large deviation for sums of long-tailed claims in a multi-risk model," Statistics & Probability Letters, Elsevier, vol. 82(7), pages 1242-1250.
    11. Liu, Yan, 2007. "Precise large deviations for negatively associated random variables with consistently varying tails," Statistics & Probability Letters, Elsevier, vol. 77(2), pages 181-189, January.
    12. Leipus, Remigijus & Siaulys, Jonas, 2007. "Asymptotic behaviour of the finite-time ruin probability under subexponential claim sizes," Insurance: Mathematics and Economics, Elsevier, vol. 40(3), pages 498-508, May.
    13. Lin, Jianxi, 2008. "The general principle for precise large deviations of heavy-tailed random sums," Statistics & Probability Letters, Elsevier, vol. 78(6), pages 749-758, April.
    14. Kaas, Rob & Tang, Qihe, 2005. "A large deviation result for aggregate claims with dependent claim occurrences," Insurance: Mathematics and Economics, Elsevier, vol. 36(3), pages 251-259, June.

    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:stapro:v:52:y:2001:i:1:p:91-100. See general information about how to correct material in RePEc.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Dana Niculescu). General contact details of provider: http://www.elsevier.com/wps/find/journaldescription.cws_home/622892/description#description .

    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.

    We have no references for this item. You can help adding them by using 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.

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

    IDEAS is a RePEc service hosted by the Research Division of the Federal Reserve Bank of St. Louis . RePEc uses bibliographic data supplied by the respective publishers.