IDEAS home Printed from https://ideas.repec.org/a/eee/stapro/v84y2014icp60-66.html
   My bibliography  Save this article

Max-sum equivalence of conditionally dependent random variables

Author

Listed:
  • Jiang, Tao
  • Gao, Qingwu
  • Wang, Yuebao

Abstract

In this paper, we prove the max-sum equivalence of random variables satisfying two conditional dependence assumptions. Besides, we also discuss the interrelationship between the above two conditional dependence assumptions. The obtained results improve and generalize some existing results.

Suggested Citation

  • Jiang, Tao & Gao, Qingwu & Wang, Yuebao, 2014. "Max-sum equivalence of conditionally dependent random variables," Statistics & Probability Letters, Elsevier, vol. 84(C), pages 60-66.
    • Handle: RePEc:eee:stapro:v:84:y:2014:i:c:p:60-66
    DOI: 10.1016/j.spl.2013.09.031
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0167715213003295
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.spl.2013.09.031?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. 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.
    2. Asmussen, Søren & Rojas-Nandayapa, Leonardo, 2008. "Asymptotics of sums of lognormal random variables with Gaussian copula," Statistics & Probability Letters, Elsevier, vol. 78(16), pages 2709-2714, November.
    3. Li, Jinzhu, 2013. "On pairwise quasi-asymptotically independent random variables and their applications," Statistics & Probability Letters, Elsevier, vol. 83(9), pages 2081-2087.
    4. Yang, Yang & Hashorva, Enkelejd, 2013. "Extremes and products of multivariate AC-product risks," Insurance: Mathematics and Economics, Elsevier, vol. 52(2), pages 312-319.
    5. Liu, Xijun & Gao, Qingwu & Wang, Yuebao, 2012. "A note on a dependent risk model with constant interest rate," Statistics & Probability Letters, Elsevier, vol. 82(4), pages 707-712.
    6. Dominik Kortschak & Hansjörg Albrecher, 2009. "Asymptotic Results for the Sum of Dependent Non-identically Distributed Random Variables," Methodology and Computing in Applied Probability, Springer, vol. 11(3), pages 279-306, September.
    7. Lin, Jianxi & Wang, Yuebao, 2012. "New examples of heavy-tailed O-subexponential distributions and related closure properties," Statistics & Probability Letters, Elsevier, vol. 82(3), pages 427-432.
    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. Hashorva, Enkelejd & Kortschak, Dominik, 2014. "Tail asymptotics of random sum and maximum of log-normal risks," Statistics & Probability Letters, Elsevier, vol. 87(C), pages 167-174.

    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. Peter Tankov, 2014. "Tails of weakly dependent random vectors," Papers 1402.4683, arXiv.org, revised Jan 2016.
    2. Archil Gulisashvili & Peter Tankov, 2013. "Tail behavior of sums and differences of log-normal random variables," Papers 1309.3057, arXiv.org, revised Jan 2016.
    3. 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.
    4. Coqueret, Guillaume, 2014. "Second order risk aggregation with the Bernstein copula," Insurance: Mathematics and Economics, Elsevier, vol. 58(C), pages 150-158.
    5. Xiaoou Li & Jingchen Liu & Gongjun Xu, 2016. "On the Tail Probabilities of Aggregated Lognormal Random Fields with Small Noise," Mathematics of Operations Research, INFORMS, vol. 41(1), pages 236-246, February.
    6. Hongmin Xiao & Lin Xie, 2018. "Asymptotic Ruin Probability of a Bidimensional Risk Model Based on Entrance Processes with Constant Interest Rate," Risks, MDPI, vol. 6(4), pages 1-12, November.
    7. Yang Yang & Xinzhi Wang & Xiaonan Su & Aili Zhang, 2019. "Asymptotic Behavior of Ruin Probabilities in an Insurance Risk Model with Quasi-Asymptotically Independent or Bivariate Regularly Varying-Tailed Main Claim and By-Claim," Complexity, Hindawi, vol. 2019, pages 1-6, October.
    8. Jaunė, Eglė & Šiaulys, Jonas, 2022. "Asymptotic risk decomposition for regularly varying distributions with tail dependence," Applied Mathematics and Computation, Elsevier, vol. 427(C).
    9. Zhang, Chenhua, 2014. "Uniform asymptotics for the tail probability of weighted sums with heavy tails," Statistics & Probability Letters, Elsevier, vol. 94(C), pages 221-229.
    10. Asimit, Alexandru V. & Furman, Edward & Tang, Qihe & Vernic, Raluca, 2011. "Asymptotics for risk capital allocations based on Conditional Tail Expectation," Insurance: Mathematics and Economics, Elsevier, vol. 49(3), pages 310-324.
    11. Søren Asmussen & Jens Ledet Jensen & Leonardo Rojas-Nandayapa, 2016. "Exponential Family Techniques for the Lognormal Left Tail," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 43(3), pages 774-787, September.
    12. Vernic, Raluca, 2018. "On the evaluation of some multivariate compound distributions with Sarmanov’s counting distribution," Insurance: Mathematics and Economics, Elsevier, vol. 79(C), pages 184-193.
    13. 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.
    14. Archil Gulisashvili & Peter Tankov, 2014. "Implied volatility of basket options at extreme strikes," Papers 1406.0394, arXiv.org.
    15. Cuberos A. & Masiello E. & Maume-Deschamps V., 2015. "High level quantile approximations of sums of risks," Dependence Modeling, De Gruyter, vol. 3(1), pages 1-18, October.
    16. Harry Joe & Haijun Li, 2011. "Tail Risk of Multivariate Regular Variation," Methodology and Computing in Applied Probability, Springer, vol. 13(4), pages 671-693, December.
    17. Søren Asmussen & José Blanchet & Sandeep Juneja & Leonardo Rojas-Nandayapa, 2011. "Efficient simulation of tail probabilities of sums of correlated lognormals," Annals of Operations Research, Springer, vol. 189(1), pages 5-23, September.
    18. Xuejun Wang & Xin Deng & Shuhe Hu, 2018. "On consistency of the weighted least squares estimators in a semiparametric regression model," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 81(7), pages 797-820, October.
    19. 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.
    20. Li, Haijun & Wu, Peiling, 2013. "Extremal dependence of copulas: A tail density approach," Journal of Multivariate Analysis, Elsevier, vol. 114(C), pages 99-111.

    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:84:y:2014:i:c:p:60-66. 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.