Marcin Topolewski

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The work concerns the applicability of credibility estimators of order higher than one, called hierarchical estimators, to posterior estimates of claim ratio in motor insurance systems based on the history of the insured. The first part presents the idea of the credibility estimation method. In the second part the linear credibility estimator is discussed. The third part introduces appropriate for risk models in the form of claims distributions, which are used to derive the corresponding hierarchical estimates of the first order. The fourth section expands the discussion of the hierarchical estimators of the order two. In the empirical fifth part previously presented solutions are used to estimate the loss ratio for the sample insurance portfolio, results are discussed and conclusions concerning the possibility of application of second order hierarchical estimators into motor insurance are formulated.


automobile insurance, credibility, hierarchical estimators


Hossack I. B., Pollard J. H., Zehnwirth B., (1983), Introductory Statistics with Applications in General Insurance, Cambrige Uniwersity Press.

Jasiulewicz H., (2005), Teoria zaufania. Modele aktuarialne, Wydawnictwo AE im. Oskara Langego we Wrocławiu, Wrocław.

Jewell W. S., (1974), Credible Means Are Exact Bayesian for Exponential Families, ASTIN Bulletin 8 (1), 77–90.

Jewell W. S., (1975), The Use of Collateral Data in Credibility Theory: A Hierarchical Model, Research Memorandum of the International Institute for Applied Systems Analysis, 24, Laxenburg, Austria.

Lemaire J., (1985), Automobile Insurance: Actuarial Models, Kluwer Nijhoff, Boston.

Norberg R., (1979), The Credibility Approach to Experience Rating, Scandinavian Actuarial Journal, 181–221.

Szymańska A., (2014), Statystyczna analiza systemów bonus-malus w ubezpieczeniach komunikacyjnych, Wydawnictwo Uniwersytetu Łódzkiego, Łódź.

Taylor G. C., (1979), Credibility Analysis of a General Hierarchical Model, Scandinavian Actuarial Journal, 1–12.

Willmot G. E., (1987), The Poisson-Inverse Gaussian Distribution as an Alternative to Negative Binominal, Scandinavian Actuarial Journal, 113–127.

Zehnwirth B., (1977), The Mean Credibility Formula is a Bayes Rule, Scandinavian Actuarial Journal, 212–216.

Zehnwirth B., (1979), A Hierarchical Model for the Estimation of Claim Rates in a Motor Car Insurance Portfolio, Scandinavian Actuarial Journal, 75–82.

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