IDEAS home Printed from https://ideas.repec.org/a/eee/insuma/v51y2012i2p472-479.html
   My bibliography  Save this article

Asymptotic consistency and inconsistency of the chain ladder

Author

Listed:
  • Pešta, Michal
  • Hudecová, Šárka

Abstract

The distribution-free chain ladder reserving method belongs to the most frequently used approaches in general insurance. It is well known, see Mack (1993), that the estimators f̂j of the development factors are unbiased and mutually uncorrelated under some mild conditions on the mean structure and under the assumption of independence of the claims in different accident years. In this article we deal with some asymptotic properties of f̂j. Necessary and sufficient conditions for asymptotic consistency of the estimators of true development factors fj are provided. A rate of convergence for the consistency is derived. Possible violation of these conditions and its consequences are discussed, and some practical recommendations are given. Numerical simulations and a real data example are provided as well.

Suggested Citation

  • Pešta, Michal & Hudecová, Šárka, 2012. "Asymptotic consistency and inconsistency of the chain ladder," Insurance: Mathematics and Economics, Elsevier, vol. 51(2), pages 472-479.
  • Handle: RePEc:eee:insuma:v:51:y:2012:i:2:p:472-479
    DOI: 10.1016/j.insmatheco.2012.07.004
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0167668712000832
    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. England, P.D. & Verrall, R.J., 2002. "Stochastic Claims Reserving in General Insurance," British Actuarial Journal, Cambridge University Press, vol. 8(03), pages 443-518, August.
    2. Renshaw, A.E. & Verrall, R.J., 1998. "A Stochastic Model Underlying the Chain-Ladder Technique," British Actuarial Journal, Cambridge University Press, vol. 4(04), pages 903-923, October.
    3. Mack, Thomas, 1993. "Distribution-free Calculation of the Standard Error of Chain Ladder Reserve Estimates," ASTIN Bulletin: The Journal of the International Actuarial Association, Cambridge University Press, vol. 23(02), pages 213-225, November.
    4. Taylor, G. C. & Ashe, F. R., 1983. "Second moments of estimates of outstanding claims," Journal of Econometrics, Elsevier, vol. 23(1), pages 37-61, 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. Hudecová, Šárka & Pešta, Michal, 2013. "Modeling dependencies in claims reserving with GEE," Insurance: Mathematics and Economics, Elsevier, vol. 53(3), pages 786-794.
    2. Mat'uv{s} Maciak & Ostap Okhrin & Michal Pev{s}ta, 2018. "Dynamic and granular loss reserving with copulae," Papers 1801.01792, arXiv.org.
    3. Pešta, Michal & Okhrin, Ostap, 2014. "Conditional least squares and copulae in claims reserving for a single line of business," Insurance: Mathematics and Economics, Elsevier, vol. 56(C), pages 28-37.

    More about this item

    Keywords

    IM10; IM20; Claims reserving; Chain ladder; Asymptotic properties; Development factors;

    JEL classification:

    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C18 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Methodolical Issues: General
    • G22 - Financial Economics - - Financial Institutions and Services - - - Insurance; Insurance Companies; Actuarial Studies

    Statistics

    Access and download statistics

    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:insuma:v:51:y:2012:i:2:p:472-479. 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/locate/inca/505554 .

    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.