IDEAS home Printed from https://ideas.repec.org/a/eee/stapro/v153y2019icp37-47.html
   My bibliography  Save this article

Second order tail approximation for the maxima of randomly weighted sums with applications to ruin theory and numerical examples

Author

Listed:
  • Lin, Jianxi

Abstract

In this paper the second order asymptotics for the tail probability of the maxima of randomly weighted sums is established under the assumption that the underlying primary random variables have a regularly varying density as x tends to infinity. In doing so, some mild conditions are imposed on the tails of the random weights, and no any assumption is made on the dependence structure between these weights. What is more, an application to insurance risk theory is presented and some numerical examples are given to show the accuracy of the second order results.

Suggested Citation

  • Lin, Jianxi, 2019. "Second order tail approximation for the maxima of randomly weighted sums with applications to ruin theory and numerical examples," Statistics & Probability Letters, Elsevier, vol. 153(C), pages 37-47.
    • Handle: RePEc:eee:stapro:v:153:y:2019:i:c:p:37-47
    DOI: 10.1016/j.spl.2019.05.015
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0167715219301440
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.spl.2019.05.015?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. Zhang, Yi & Shen, Xinmei & Weng, Chengguo, 2009. "Approximation of the tail probability of randomly weighted sums and applications," Stochastic Processes and their Applications, Elsevier, vol. 119(2), pages 655-675, February.
    2. Li, Jinzhu, 2018. "On the joint tail behavior of randomly weighted sums of heavy-tailed random variables," Journal of Multivariate Analysis, Elsevier, vol. 164(C), pages 40-53.
    3. Lin, Jianxi, 2012. "Second order asymptotics for ruin probabilities in a renewal risk model with heavy-tailed claims," Insurance: Mathematics and Economics, Elsevier, vol. 51(2), pages 422-429.
    4. Tang, Qihe & Tsitsiashvili, Gurami, 2003. "Precise estimates for the ruin probability in finite horizon in a discrete-time model with heavy-tailed insurance and financial risks," Stochastic Processes and their Applications, Elsevier, vol. 108(2), pages 299-325, December.
    5. Qingwu Gao & Na Jin, 2015. "Randomly Weighted Sums of Pairwise Quasi Upper-Tail Independent Increments with Application to Risk Theory," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 44(18), pages 3885-3902, September.
    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. Yang Yang & Shuang Liu & Kam Chuen Yuen, 2022. "Second-Order Tail Behavior for Stochastic Discounted Value of Aggregate Net Losses in a Discrete-Time Risk Model," Journal of Theoretical Probability, Springer, vol. 35(4), pages 2600-2621, December.
    2. 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.

    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. 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.
    2. Xinmei Shen & Kailin Du, 2023. "Uniform Approximation for the Tail Behavior of Bidimensional Randomly Weighted Sums," Methodology and Computing in Applied Probability, Springer, vol. 25(1), pages 1-25, March.
    3. Chen, Yiqing, 2020. "A Kesten-type bound for sums of randomly weighted subexponential random variables," Statistics & Probability Letters, Elsevier, vol. 158(C).
    4. Tang, Qihe & Wang, Guojing & Yuen, Kam C., 2010. "Uniform tail asymptotics for the stochastic present value of aggregate claims in the renewal risk model," Insurance: Mathematics and Economics, Elsevier, vol. 46(2), pages 362-370, April.
    5. 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.
    6. Chen Yu & Zhang Weiping & Liu Jie, 2010. "Asymptotic Tail Probability of Randomly Weighted Sum of Dependent Heavy-Tailed Random Variables," Asia-Pacific Journal of Risk and Insurance, De Gruyter, vol. 4(2), pages 1-11, July.
    7. Sun, Ying & Wei, Li, 2014. "The finite-time ruin probability with heavy-tailed and dependent insurance and financial risks," Insurance: Mathematics and Economics, Elsevier, vol. 59(C), pages 178-183.
    8. Yang, Yang & Jiang, Tao & Wang, Kaiyong & Yuen, Kam C., 2020. "Interplay of financial and insurance risks in dependent discrete-time risk models," Statistics & Probability Letters, Elsevier, vol. 162(C).
    9. Yang Yang & Shuang Liu & Kam Chuen Yuen, 2022. "Second-Order Tail Behavior for Stochastic Discounted Value of Aggregate Net Losses in a Discrete-Time Risk Model," Journal of Theoretical Probability, Springer, vol. 35(4), pages 2600-2621, December.
    10. Li, Jinzhu, 2018. "On the joint tail behavior of randomly weighted sums of heavy-tailed random variables," Journal of Multivariate Analysis, Elsevier, vol. 164(C), pages 40-53.
    11. Eckert, Johanna & Gatzert, Nadine, 2018. "Risk- and value-based management for non-life insurers under solvency constraints," European Journal of Operational Research, Elsevier, vol. 266(2), pages 761-774.
    12. 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.
    13. 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.
    14. Cai, Jun & Dickson, David C.M., 2004. "Ruin probabilities with a Markov chain interest model," Insurance: Mathematics and Economics, Elsevier, vol. 35(3), pages 513-525, December.
    15. 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.
    16. 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.
    17. 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.
    18. 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.
    19. Yang, Yang & Leipus, Remigijus & Šiaulys, Jonas, 2014. "Closure property and maximum of randomly weighted sums with heavy-tailed increments," Statistics & Probability Letters, Elsevier, vol. 91(C), pages 162-170.
    20. Wang, Dingcheng & Chen, Pingyan & Su, Chun, 2007. "The supremum of random walk with negatively associated and heavy-tailed steps," Statistics & Probability Letters, Elsevier, vol. 77(13), pages 1403-1412, July.

    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:153:y:2019:i:c:p:37-47. 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/wps/find/journaldescription.cws_home/622892/description#description .

    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.