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Estimation of the heterogeneity parameter in the Bühlmann-Straub credibility theory model. (English) Zbl 0745.62097

Summary: We consider the Bühlmann-Straub model in credibility theory with parameters \(s^ 2\), measuring the variability of the observations in the contracts and \(a\), measuring the heterogeneity of the portfolio. For each approximation \((s'{}^ 2,a')\) of \((s^ 2,a)\), we define an unbiased estimator \(\hat a'\) of \(a\). In fact \(\hat a'\) is nothing less than the classical Bichsel-Straub pseudo-estimator transformed in such a way that the pseudo character, i.e. the dependence on the value to be estimated, is eliminated. This value may be replaced by an approximation and \(\hat a'\) is unbiased whatever be that approximation.

MSC:

62P05 Applications of statistics to actuarial sciences and financial mathematics
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References:

[1] Bichsel, F. and E. Straub. Erfahrungstarifierung in der Kollektiv-Krankenversicherung. Unpublished.; Bichsel, F. and E. Straub. Erfahrungstarifierung in der Kollektiv-Krankenversicherung. Unpublished.
[2] Bühlmann, H.; Straub, E., Glaubwürdigkeit für Schadensätze, MVSV, 70, 1, 111-133 (1976) · Zbl 0197.46502
[3] De Vylder, F. and M. Goovaerts. Optimal parameter estimation under zero excess assumptions in a classical model. Forthcoming a.; De Vylder, F. and M. Goovaerts. Optimal parameter estimation under zero excess assumptions in a classical model. Forthcoming a. · Zbl 0752.62076
[4] De Vylder, F. and M. Goovaerts. Optimal parameter estimation under zero excess assumptions in the Bühlmann—Straub model. Forthcoming b.; De Vylder, F. and M. Goovaerts. Optimal parameter estimation under zero excess assumptions in the Bühlmann—Straub model. Forthcoming b. · Zbl 0783.62088
[5] Dubey, A.; Gisler, A., On parameter estimation in credibility, MVSV, 81, 1, 187-212 (1981) · Zbl 0482.62092
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