IDEAS home Printed from https://ideas.repec.org/p/cte/wsrepe/4509.html
   My bibliography  Save this paper

On credibility and robustness with the Kalman filter

Author

Listed:
  • Garrido, José
  • Romera, Rosario

Abstract

Bühlmann (1967) gave a formal Bayesian derivation of the credibility ratio estimators that actuaries had been using for many years. Since then various generalizations of Bühlmann's model have appeared in the literature, each relaxing the i.i.d. assumptions in its own way. The introduction of weights is due to Bülhmann & Straub (1970) and that the regressors to Hachemeister (1975), but the first comprehensive actuarial application of the Kalman filter is due to de Jong & Zehnwirth (1983). More recent efforts have concentrated on the robustification of these estimators, as they provedı to be extremely sensitive to large claims. Kremer (1991) studies a robust regression credibility model and Künsch (1992) tackles the weighted case. Following Kremer (1994) we propose here a robust Kalman filter credibility model.

Suggested Citation

  • Garrido, José & Romera, Rosario, 1995. "On credibility and robustness with the Kalman filter," DES - Working Papers. Statistics and Econometrics. WS 4509, Universidad Carlos III de Madrid. Departamento de Estadística.
    • Handle: RePEc:cte:wsrepe:4509
    as

    Download full text from publisher

    File URL: https://e-archivo.uc3m.es/rest/api/core/bitstreams/3bd14d82-b57b-4edf-8689-037a99ba494d/content
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Kremer, Erhard, 1994. "Robust Credibility via Robust Kalman Filtering," ASTIN Bulletin, Cambridge University Press, vol. 24(2), pages 221-233, November.
    2. Gisler, Alois & Reinhard, Peter, 1993. "Robust Credibility1," ASTIN Bulletin, Cambridge University Press, vol. 23(1), pages 117-143, May.
    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. Pitselis, Georgios, 2008. "Robust regression credibility: The influence function approach," Insurance: Mathematics and Economics, Elsevier, vol. 42(1), pages 288-300, February.
    2. Pitselis, Georgios, 2004. "A seemingly unrelated regression model in a credibility framework," Insurance: Mathematics and Economics, Elsevier, vol. 34(1), pages 37-54, February.
    3. Dornheim, Harald & Brazauskas, Vytaras, 2011. "Robust-efficient credibility models with heavy-tailed claims: A mixed linear models perspective," Insurance: Mathematics and Economics, Elsevier, vol. 48(1), pages 72-84, January.
    4. Helena Jasiulewicz, 2013. "Przestrzeń stanów i filtr Kalmana w teorii ubezpieczeń," Collegium of Economic Analysis Annals, Warsaw School of Economics, Collegium of Economic Analysis, issue 31, pages 101-116.
    5. Agustin Hernandez Bastida & Emilio Gomez Deniz & Jose Maria Perez Sanchez, 2009. "Bayesian robustness of the compound Poisson distribution under bidimensional prior: an application to the collective risk model," Journal of Applied Statistics, Taylor & Francis Journals, vol. 36(8), pages 853-869.
    6. Pitselis, Georgios, 2013. "Pure robust versus robust portfolio unbiased—Credibility and asymptotic optimality," Insurance: Mathematics and Economics, Elsevier, vol. 52(2), pages 391-403.

    More about this item

    Keywords

    Credibility;

    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:cte:wsrepe:4509. 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: Ana Poveda (email available below). General contact details of provider: http://portal.uc3m.es/portal/page/portal/dpto_estadistica .

    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.