IDEAS home Printed from https://ideas.repec.org/a/eee/insuma/v42y2008i1p378-388.html
   My bibliography  Save this article

Prediction error in the chain ladder method

Author

Listed:
  • Wüthrich, Mario V.

Abstract

We define a chain ladder model which allows for the study of three different error types: (a) diversifiable process error, (b) non-diversifiable process error, and (c) parameter estimation error. The model is based on the classical stochastic chain ladder model introduced by Mack [Mack, T., 1993. Distribution-free calculation of the standard error of chain ladder reserve estimates. Astin Bull. 23(2), 213-225]. In order to clearly distinguish the different sources of prediction uncertainty, we have to slightly modify that classical chain ladder model.

Suggested Citation

  • Wüthrich, Mario V., 2008. "Prediction error in the chain ladder method," Insurance: Mathematics and Economics, Elsevier, vol. 42(1), pages 378-388, February.
    • Handle: RePEc:eee:insuma:v:42:y:2008:i:1:p:378-388
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0167-6687(07)00052-2
    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. Gisler, Alois, 2006. "The Estimation Error in the Chain-Ladder Reserving Method: A Bayesian Approach," ASTIN Bulletin, Cambridge University Press, vol. 36(2), pages 554-565, November.
    2. Buchwalder, Markus & Bühlmann, Hans & Merz, Michael & Wüthrich, Mario V., 2006. "The Mean Square Error of Prediction in the Chain Ladder Reserving Method (Mack and Murphy Revisited)," ASTIN Bulletin, Cambridge University Press, vol. 36(2), pages 521-542, November.
    3. Venter, Gary G., 2006. "Discussion of the Mean Square Error of Prediction in the Chain Ladder Reserving Method," ASTIN Bulletin, Cambridge University Press, vol. 36(2), pages 566-571, November.
    4. Mack, Thomas, 1993. "Distribution-free Calculation of the Standard Error of Chain Ladder Reserve Estimates," ASTIN Bulletin, Cambridge University Press, vol. 23(2), pages 213-225, November.
    Full references (including those not matched with items on IDEAS)

    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. Nils Engler & Filip Lindskog, 2023. "Mack's estimator motivated by large exposure asymptotics in a compound Poisson setting," Papers 2310.12056, arXiv.org.
    2. Diers, Dorothea & Linde, Marc & Hahn, Lukas, 2016. "Addendum to ‘The multi-year non-life insurance risk in the additive reserving model’ [Insurance Math. Econom. 52(3) (2013) 590–598]: Quantification of multi-year non-life insurance risk in chain ladde," Insurance: Mathematics and Economics, Elsevier, vol. 67(C), pages 187-199.
    3. Boratyńska, Agata, 2017. "Robust Bayesian estimation and prediction of reserves in exponential model with quadratic variance function," Insurance: Mathematics and Economics, Elsevier, vol. 76(C), pages 135-140.
    4. 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.
    5. Peters, Gareth W. & Targino, Rodrigo S. & Wüthrich, Mario V., 2017. "Full Bayesian analysis of claims reserving uncertainty," Insurance: Mathematics and Economics, Elsevier, vol. 73(C), pages 41-53.
    6. Portugal, Luís & Pantelous, Athanasios A. & Verrall, Richard, 2021. "Univariate and multivariate claims reserving with Generalized Link Ratios," Insurance: Mathematics and Economics, Elsevier, vol. 97(C), pages 57-67.
    7. Lindholm, Mathias & Verrall, Richard, 2020. "Regression based reserving models and partial information," Insurance: Mathematics and Economics, Elsevier, vol. 94(C), pages 109-124.
    8. Wahl, Felix & Lindholm, Mathias & Verrall, Richard, 2019. "The collective reserving model," Insurance: Mathematics and Economics, Elsevier, vol. 87(C), pages 34-50.
    9. Alexandre Boumezoued & Yoboua Angoua & Laurent Devineau & Jean-Philippe Boisseau, 2011. "One-year reserve risk including a tail factor: closed formula and bootstrap approaches," Working Papers hal-00605329, HAL.
    10. Steinmetz, Julia & Jentsch, Carsten, 2022. "Asymptotic theory for Mack's model," Insurance: Mathematics and Economics, Elsevier, vol. 107(C), pages 223-268.
    11. Fröhlich, Andreas & Weng, Annegret, 2018. "Parameter uncertainty and reserve risk under Solvency II," Insurance: Mathematics and Economics, Elsevier, vol. 81(C), pages 130-141.
    12. Hahn, Lukas, 2017. "Multi-year non-life insurance risk of dependent lines of business in the multivariate additive loss reserving model," Insurance: Mathematics and Economics, Elsevier, vol. 75(C), pages 71-81.
    13. Éva Komáromi, 2012. "Entropy programming modeling of IBNR claims reserves," Annals of Operations Research, Springer, vol. 200(1), pages 93-108, November.
    14. 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.
    15. 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.
    16. Mathias Lindholm & Felix Wahl, 2020. "On the variance parameter estimator in general linear models," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 83(2), pages 243-254, February.
    17. Alexandre Boumezoued & Yoboua Angoua & Laurent Devineau & Jean-Philippe Boisseau, 2011. "One-year reserve risk including a tail factor: closed formula and bootstrap approaches," Papers 1107.0164, arXiv.org, revised Apr 2012.
    18. COSTA, JUAN IGNACIO BACCINO & DE ARMAS, GONZALO & Álvarez-Vaz, Ramón Dr., 2022. "Estudio De Algunos Métodos De Reservas Técnicas En Condiciones De Incertidumbre Para Seguros De No Vida (Study Of Some Methods Of Technical Reserves Under Conditions Of Uncertainty For Non-Life Insura," OSF Preprints 3pjr9, Center for Open Science.
    19. Emmanuel Jordy Menvouta & Jolien Ponnet & Robin Van Oirbeek & Tim Verdonck, 2022. "mCube: Multinomial Micro-level reserving Model," Papers 2212.00101, arXiv.org.
    20. Gian Paolo Clemente & Nino Savelli & Diego Zappa, 2019. "Modelling Outstanding Claims with Mixed Compound Processes in Insurance," International Business Research, Canadian Center of Science and Education, vol. 12(3), pages 123-138, March.

    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:eee:insuma:v:42:y:2008:i:1:p:378-388. 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/locate/inca/505554 .

    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.