IDEAS home Printed from https://ideas.repec.org/a/spr/jotpro/v25y2012i4d10.1007_s10959-011-0367-2.html
   My bibliography  Save this article

Precise Large Deviations for Long-Tailed Distributions

Author

Listed:
  • Fotis Loukissas

    (University of the Aegean)

Abstract

In this paper, we investigate the precise large deviations for sums of independent identically distributed random variables with heavy-tailed distributions. We prove asymptotic relations for non-random sums and for random sums of random variables with long-tailed distributions. We apply the results on two useful counting processes, namely, renewal and compound-renewal processes.

Suggested Citation

  • Fotis Loukissas, 2012. "Precise Large Deviations for Long-Tailed Distributions," Journal of Theoretical Probability, Springer, vol. 25(4), pages 913-924, December.
    • Handle: RePEc:spr:jotpro:v:25:y:2012:i:4:d:10.1007_s10959-011-0367-2
    DOI: 10.1007/s10959-011-0367-2
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10959-011-0367-2
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s10959-011-0367-2?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. Cline, D. B. H. & Samorodnitsky, G., 1994. "Subexponentiality of the product of independent random variables," Stochastic Processes and their Applications, Elsevier, vol. 49(1), pages 75-98, January.
    2. 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.
    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. Robert, Christian Y. & Segers, Johan, 2008. "Tails of random sums of a heavy-tailed number of light-tailed terms," Insurance: Mathematics and Economics, Elsevier, vol. 43(1), pages 85-92, August.
    2. Yiqing Chen & Kam C. Yuen & Kai W. Ng, 2011. "Precise Large Deviations of Random Sums in Presence of Negative Dependence and Consistent Variation," Methodology and Computing in Applied Probability, Springer, vol. 13(4), pages 821-833, December.
    3. Christian Y. Robert & Johan Segers, 2007. "Tails of random sums of a heavy-tailed number of light-tailed terms," Papers math/0703022, arXiv.org, revised Oct 2007.
    4. Chen, Yiqing & Ng, Kai W., 2007. "The ruin probability of the renewal model with constant interest force and negatively dependent heavy-tailed claims," Insurance: Mathematics and Economics, Elsevier, vol. 40(3), pages 415-423, May.
    5. Yang, Haizhong & Sun, Suting, 2013. "Subexponentiality of the product of dependent random variables," Statistics & Probability Letters, Elsevier, vol. 83(9), pages 2039-2044.
    6. Serguei Foss & Andrew Richards, 2010. "On Sums of Conditionally Independent Subexponential Random Variables," Mathematics of Operations Research, INFORMS, vol. 35(1), pages 102-119, February.
    7. Yang, Yingying & Hu, Shuhe & Wu, Tao, 2011. "The tail probability of the product of dependent random variables from max-domains of attraction," Statistics & Probability Letters, Elsevier, vol. 81(12), pages 1876-1882.
    8. Robert, Christian Y., 2013. "Some new classes of stationary max-stable random fields," Statistics & Probability Letters, Elsevier, vol. 83(6), pages 1496-1503.
    9. Shen, Xinmei & Lin, Zhengyan, 2008. "Precise large deviations for randomly weighted sums of negatively dependent random variables with consistently varying tails," Statistics & Probability Letters, Elsevier, vol. 78(18), pages 3222-3229, December.
    10. 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.
    11. 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.
    12. Jiang, Tao & Wang, Yuebao & Chen, Yang & Xu, Hui, 2015. "Uniform asymptotic estimate for finite-time ruin probabilities of a time-dependent bidimensional renewal model," Insurance: Mathematics and Economics, Elsevier, vol. 64(C), pages 45-53.
    13. Yang, Yang & Hashorva, Enkelejd, 2013. "Extremes and products of multivariate AC-product risks," Insurance: Mathematics and Economics, Elsevier, vol. 52(2), pages 312-319.
    14. Dan Zhu & Ming Zhou & Chuancun Yin, 2023. "Finite-Time Ruin Probabilities of Bidimensional Risk Models with Correlated Brownian Motions," Mathematics, MDPI, vol. 11(12), pages 1-18, June.
    15. Gao, Qingwu & Liu, Xijun, 2013. "Uniform asymptotics for the finite-time ruin probability with upper tail asymptotically independent claims and constant force of interest," Statistics & Probability Letters, Elsevier, vol. 83(6), pages 1527-1538.
    16. 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.
    17. Yang Yang & Xinzhi Wang & Shaoying Chen, 2022. "Second Order Asymptotics for Infinite-Time Ruin Probability in a Compound Renewal Risk Model," Methodology and Computing in Applied Probability, Springer, vol. 24(2), pages 1221-1236, June.
    18. Peng, Jiangyan & Huang, Jin, 2010. "Ruin probability in a one-sided linear model with constant interest rate," Statistics & Probability Letters, Elsevier, vol. 80(7-8), pages 662-669, April.
    19. Jiang, Jun & Tang, Qihe, 2011. "The product of two dependent random variables with regularly varying or rapidly varying tails," Statistics & Probability Letters, Elsevier, vol. 81(8), pages 957-961, August.
    20. Wang, Yinfeng & Yin, Chuancun, 2010. "Approximation for the ruin probabilities in a discrete time risk model with dependent risks," Statistics & Probability Letters, Elsevier, vol. 80(17-18), pages 1335-1342, September.

    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:spr:jotpro:v:25:y:2012:i:4:d:10.1007_s10959-011-0367-2. 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: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.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.