Bauwelinckx, T.; Labie, E.; Goovaerts, M. J. A new approach for loaded credibility premiums. (English) Zbl 0738.62096 J. Comput. Appl. Math. 37, No. 1-3, 301-314 (1991). Summary: A new technique is developed for estimating credibility premiums for risks, containing a fraction of the variance of the risk as loading on the net risk premium. This method provided us with another approach to the known results for credibility loaded premiums, not having the drawback of estimating an approximation of the so-called fluctuation part. In addition, the present investigation provides us with an elegant extension to loaded premiums in the hierarchical credibility model. The results are obtained in the framework of semilinear hierarchical credibility theory. As a byproduct the so-called optimal semilinear credibility result is extended to the case of Esscher premiums. In this contribution also the pseudo-estimators, to be solved iteratively for the structural parameters appearing in the variance-loaded model, are given. MSC: 62P05 Applications of statistics to actuarial sciences and financial mathematics 91B30 Risk theory, insurance (MSC2010) Keywords:estimating credibility premiums for risks; credibility loaded premiums; semilinear hierarchical credibility; optimal semilinear credibility result; Esscher premiums; pseudo-estimators; variance-loaded model PDFBibTeX XMLCite \textit{T. Bauwelinckx} et al., J. Comput. Appl. Math. 37, No. 1--3, 301--314 (1991; Zbl 0738.62096) Full Text: DOI References: [1] Bauwelinckx, T., Numerical evaluation of loaded credibility premiums (1990), Kath. Univ: Kath. Univ Leuven · Zbl 0714.62100 [2] Bauwelinckx, T.; Goovaerts, M. J., On a multilevel hierarchical credibility algorithm, Insurance Math. Econom., 9, 2/3, 221-228 (1990) · Zbl 0714.62100 [3] Bühlmann, H., Mathematical Methods in Risk Theory (1970), Springer: Springer Berlin · Zbl 0209.23302 [4] de Lourdes, M. Centeno, The Bühlmann-Straub Model with premium calculated according to the variance princple, Insurance Math. Econom., 8, 1, 3-10 (1989) · Zbl 0701.62101 [5] De Vylder, F., Optimal semilinear credibility, Mitt. Verein Schweiz. Versicherungsmath., 76, 17-40 (1976) · Zbl 0329.62077 [6] De Vylder, F.; Goovaerts, M. J., Semilinear credibility with several approximating functions, Insurance Math. Econom., 4, 3, 155-162 (1985) · Zbl 0571.62095 [7] Gerber, H., Credibility for Esscher premiums, Mitt. Verein. Schweiz. Versicherungsmath, 80, 307-312 (1980) · Zbl 0446.62110 [8] Goovaerts, M. J.; Kaas, R.; van Heerwaarden, A. E.; Bauwelinckx, T., Effective Actuarial Methods, 3 (1990), North-Holland: North-Holland Amsterdam, Insurance Ser. 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.