Practical Models in Credibility Theory, Including Parameter Estimation

  • F. de Vylder
Chapter
Part of the NATO ASI Series book series (ASIC, volume 121)

Abstract

In credibility theory, an unobservable random vector Ŷ is approximated by a random vector Ŷ in a pre-assigned set A of admitted estimators for Y. The credibility approximation Ŷ for Y is best in the sense that it is the vector VεA minimizing the distance d(V,Y) between V and Y.

Several models in credibility theory (depending onA , d and the set of all involved random variable) have been developed in recent years. The starting point of modern credibility theory is model by Bühlmann (1967). This model has been generalized in several directions. We only retain the models having already proved their practical usefulness and, among the newer models, those that we believe to be most promising for future applications. These are:

  • The time-homogeneous model with unweighted observations (Bülhmann, 1967).

  • The time-homgeneous model weigthed observations (Bülhmann, 1970)

  • The regression model (Hachemeister, 1975)

  • The regression model with scalar credibility weights (De Vylder, to be published)

  • A multiplicative model (De Vylder, submitted for publication)

Our approach has a geometrical character. The vector Y shall be a point in a Hilber space H and A shall be a closed convex set in H. The Ŷ shall be the orthogonal projection of Y on A.

The credibility estimator Ŷ depends on observable random variables but also unknown structure parameters. In the practical models, the latter can be estimated from realizations of the observable random variables.

Keywords

Hilbert Space Unbiased Estimator Initial Space Credibility Theory Credibility Estimator 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
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References

  1. Bühlmann H. (1967), Experience rating and credibility. ASTIN Bulletin 4 199–207.Google Scholar
  2. Bühlmann H. & Straub E. (1970). Glaübwurdigkeit für Schaden- sätze. Mitt, der Ver. Schweiz. Vers. Math., p. 11–133.Google Scholar
  3. De Vylder F. (1976). Geometrical credibility. Scandinavian Actuarial Journal, p. 121–149.Google Scholar
  4. De Vylder F. (to be published). Practical credibility theory with emphasis on optimal parameter estimation. ASTIN Bulletin.Google Scholar
  5. De Vylder F. (to be published). Regression model with scalar credibility weights. Mitt. Ver. Schweiz. vers. Math.Google Scholar
  6. De Vylder F. (submitted for publication). Estimation of IBNR claims by credibility theory. Insurance.Google Scholar
  7. De Vylder F. & Sundt B. (submitted for publication). Constrained credibility estimators in the regression model. Scandinavian Actuarial Journal.Google Scholar
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Copyright information

© D. Reidel Publishing Company 1984

Authors and Affiliations

  • F. de Vylder
    • 1
  1. 1.Catholic University of LouvainLouvain-la-NeuveBelgium

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