IDEAS home Printed from https://ideas.repec.org/a/eee/stapro/v69y2004i2p117-128.html
   My bibliography  Save this article

Bivariate maximum insurance claim and related point processes

Author

Listed:
  • Hashorva, Enkelejd

Abstract

Let X1,X2,... be independent bivariate claim sizes arising from an insurance portfolio. The number of claims occurring in the time interval [0,t] is denoted by N(t). We investigate in this paper distributional and asymptotic properties of the following point process:with XN(t):N(t), the bivariate maximum insurance claim occurring during [0,t]. We show that are strongly consistent estimators of a certain tail probability of the claim size distribution. Further, we investigate the connection between convergence in distribution of the bivariate maximum claim size and weak convergence of . As a byproduct, a result for the ECOMOR reinsurance treaty is obtained.

Suggested Citation

  • Hashorva, Enkelejd, 2004. "Bivariate maximum insurance claim and related point processes," Statistics & Probability Letters, Elsevier, vol. 69(2), pages 117-128, August.
  • Handle: RePEc:eee:stapro:v:69:y:2004:i:2:p:117-128
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0167-7152(04)00163-4
    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.

    References listed on IDEAS

    as
    1. Li, Y. & Pakes, Anthony G., 2001. "On the number of near-maximum insurance claims," Insurance: Mathematics and Economics, Elsevier, vol. 28(3), pages 309-323, June.
    2. Hashorva, Enkelejd & Hüsler, Jürg, 2001. "On the number of points near the multivariate maxima," Statistics & Probability Letters, Elsevier, vol. 55(2), pages 113-124, November.
    3. Hashorva, Enkelejd, 2003. "On the number of near-maximum insurance claim under dependence," Insurance: Mathematics and Economics, Elsevier, vol. 32(1), pages 37-49, February.
    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. Dembinska, Anna & Iliopoulos, George, 2012. "On the asymptotics of numbers of observations in random regions determined by order statistics," Journal of Multivariate Analysis, Elsevier, vol. 103(1), pages 151-160, January.
    2. Bairamov, I. & Stepanov, A., 2011. "Numbers of near bivariate record-concomitant observations," Journal of Multivariate Analysis, Elsevier, vol. 102(5), pages 908-917, May.
    3. Bairamov, I. & Stepanov, A., 2010. "Numbers of near-maxima for the bivariate case," Statistics & Probability Letters, Elsevier, vol. 80(3-4), pages 196-205, February.
    4. Nadarajah, Saralees, 2013. "Expansions for bivariate extreme value distributions," Statistics & Probability Letters, Elsevier, vol. 83(3), pages 744-752.
    5. Hashorva, Enkelejd, 2007. "On the asymptotic distribution of certain bivariate reinsurance treaties," Insurance: Mathematics and Economics, Elsevier, vol. 40(2), pages 200-208, March.

    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:69:y:2004:i:2:p:117-128. 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.

    If CitEc recognized a 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.

    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.