an:04066192
Zbl 0653.62075
Mangold, Klaus-Peter
Rekursive SchĂ¤tzverfahren in der KredibilitĂ¤tstheorie. (Recursive estimation procedures in credibility theory)
DE
Bl., Dtsch. Ges. Versicherungsmath. 18, No. 1, 27-44 (1987).
0012-0200
1987
j
62P05
Hachemeister's regression model; Best affine-linear estimators; recursive computability; linear dynamic model; linear model with recursive covariance structure; time series models; algorithms; credibility estimator; Hilbert space projection; credibility models; evolutionary model; recursive formulas
Summary: Best affine-linear estimators based on observations \(\eta_ 1,...,\eta_ t\) are investigated with special regards to recursive computability. Under various specific model assumptions (linear dynamic model, linear model with recursive covariance structure, time series models), algorithms are presented and particularly their mutual correlations are shown. By identifying the classical credibility estimator as an \({\mathcal L}\) \(n_ 2\)-Hilbert space projection, easily all results can be transfered to a general credibility model.
Considering four, well-known, specific credibility models in more detail, both application of the algorithms and dissolving the normal equations leads to the solution of the credibility estimation problem. In case of \textit{C. A. Hachemeister}'s regression model [Credibility, Theory Appl. 1981, Proc. Actuarial Res. Conf., Berkeley 1974, 129-163 (1975; Zbl 0354.62057)] and also in case of \textit{B. Sundt}'s evolutionary model [Scand. Acturial J. 1981, 3-21 (1981; Zbl 0463.62093)] the recursive formulas are better suited for practical purpose.
0354.62057; 0463.62093