×

Balanced credibility estimation. (English) Zbl 0935.62119

The author deals with credibility estimation known as linear Bayes estimation which is a well-established technique in actuarial practice and shows how multivariate credibility estimators should be adjusted to satisfy a linear balancing constraint. In order to illustrate the balancing concept introduced in the paper the author begins with a very brief description of credibility estimation in the now classical Bühlmann-Straub model and considers later more general objects.
This idea is not new and has been used in the classical papers by Fl. de Vylder [Scand. Actuarial J. 1976, 121-149 (1976; Zbl 0345.62082)] and G. C. Taylor [ibid. 1977, 149-168 (1977; Zbl 0384.62083)]. But the constraints proposed in these papers differ from the constraint proposed by the author of this paper. The balance in this paper gives a self-contained derivation of optimal credibility estimation under a generalized balancing constraint.

MSC:

62P05 Applications of statistics to actuarial sciences and financial mathematics
62F15 Bayesian inference
91B30 Risk theory, insurance (MSC2010)
62G05 Nonparametric estimation
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] ’The credibility approach to experience rating’, Scand. Actuarial J., 181–221 (1979). · Zbl 0424.62071
[2] Bühlmann, Mitteilungen der Vereinigung Schweizerischer Versicherungsmathematiker 70 pp 111– (1970)
[3] ’In search of a general parameter-free credibility formula’, in (ed.), Credibility. Theory and Applications, Academic Press, 401–408, 1975.
[4] ’Geometrical credibility’, Scand. Actuarial J., 121–149 (1976). · Zbl 0345.62082
[5] ’Abstract credibility’, Scand. Actuarial J., 149–168 (1977). · Zbl 0384.62083
[6] and , ’Constrained credibility estimators in the regression model’, Scand. Actuarial J., 23–37 (1982).
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.