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On credibility and robustness with the Kalman filter

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  • 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
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    References listed on IDEAS

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    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.
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    Keywords

    Credibility;

    Statistics

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