IDEAS home Printed from https://ideas.repec.org/a/cup/astinb/v49y2019i03p787-821_00.html
   My bibliography  Save this article

The Reserve Uncertainties In The Chain Ladder Model Of Mack Revisited

Author

Listed:
  • Gisler, Alois

Abstract

We revisit the “full picture†of the claims development uncertainty in Mack’s (1993) distribution-free stochastic chain ladder model. We derive the uncertainty estimators in a new and easily understandable way, which is much simpler than the derivation found so far in the literature, and compare them with the well known estimators of Mack and of Merz–Wüthrich. Our uncertainty estimators of the one-year run-off risks are new and different to the Merz–Wüthrich formulas. But if we approximate our estimators by a first order Taylor expansion, we obtain equivalent but simpler formulas. As regards the ultimate run-off risk, we obtain the same formulas as Mack for single accident years and an equivalent but better interpretable formula for the total over all accident years.

Suggested Citation

  • Gisler, Alois, 2019. "The Reserve Uncertainties In The Chain Ladder Model Of Mack Revisited," ASTIN Bulletin, Cambridge University Press, vol. 49(3), pages 787-821, September.
    • Handle: RePEc:cup:astinb:v:49:y:2019:i:03:p:787-821_00
    as

    Download full text from publisher

    File URL: https://www.cambridge.org/core/product/identifier/S0515036119000187/type/journal_article
    File Function: link to article abstract page
    Download Restriction: no
    ---><---

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Marcin Szatkowski & Łukasz Delong, 2021. "One-Year and Ultimate Reserve Risk in Mack Chain Ladder Model," Risks, MDPI, vol. 9(9), pages 1-29, August.
    2. Steinmetz, Julia & Jentsch, Carsten, 2022. "Asymptotic theory for Mack's model," Insurance: Mathematics and Economics, Elsevier, vol. 107(C), pages 223-268.
    3. Gao, Guangyuan & Meng, Shengwang & Shi, Yanlin, 2021. "Dispersion modelling of outstanding claims with double Poisson regression models," Insurance: Mathematics and Economics, Elsevier, vol. 101(PB), pages 572-586.
    4. Nils Engler & Filip Lindskog, 2023. "Mack's estimator motivated by large exposure asymptotics in a compound Poisson setting," Papers 2310.12056, arXiv.org.
    5. Marcin Szatkowski, 2022. "Study of Actuarial Characteristics of One-Year and Ultimate Reserve Risk Distributions Based on Market Data," Central European Journal of Economic Modelling and Econometrics, Central European Journal of Economic Modelling and Econometrics, vol. 14(4), pages 225-262, December.

    More about this item

    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:cup:astinb:v:49:y:2019:i:03:p:787-821_00. 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.

    We have no bibliographic references for this item. You can help adding them by using 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: Kirk Stebbing (email available below). General contact details of provider: https://www.cambridge.org/asb .

    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.