Pierre-Loti-Viaud, Daniel Parametric credibility, correlation and bonus-malus rating. (Crédibilité paramétrique, corrélation et tarification bonus-malus.) (French) Zbl 1068.91044 C. R., Math., Acad. Sci. Paris 339, No. 4, 283-286 (2004). Summary: Is an actuarial rating of bonus-malus type based on the parametric credibility model of mixed Poisson distributions too differentiated? To answer this question, we enlarge the model of mixed Poisson distributions by considering mixed negative binomial distributions. The correlation coefficient between the annual claim numbers for an individual can then be adjusted, and we calculate the differences between the ratings coming from this new model of parametric credibility. An application of these results to a car portfolio shows that adjustment of the correlation may yield significantly smaller rating differences than those coming from the classical model. MSC: 91B30 Risk theory, insurance (MSC2010) Keywords:mixed Poisson distributions; mixed negative binomial distributions; car portfolio PDFBibTeX XMLCite \textit{D. Pierre-Loti-Viaud}, C. R., Math., Acad. Sci. Paris 339, No. 4, 283--286 (2004; Zbl 1068.91044) Full Text: DOI References: [1] Besson, J. L.; Partrat, C., Trend et systèmes de bonus-malus, ASTIN Bulletin, 22, 11-31 (1992) [2] E. Cohen, D. Pierre-Loti-Viaud, A test for assuming mixtures of Poisson distributions in a general parametric credibility system, prépublication LSTA, 2003, soumise pour publication; E. Cohen, D. Pierre-Loti-Viaud, A test for assuming mixtures of Poisson distributions in a general parametric credibility system, prépublication LSTA, 2003, soumise pour publication [3] E. Cohen, D. Pierre-Loti-Viaud, Ajustement d’un modèle de crédibilité paramétrique sur un portefeuille automobile vu pendant deux ans, prépublication LSTA, 2003; E. Cohen, D. Pierre-Loti-Viaud, Ajustement d’un modèle de crédibilité paramétrique sur un portefeuille automobile vu pendant deux ans, prépublication LSTA, 2003 [4] De Vylder, F. E., Advanced Risk Theory (1996), Éditions de l’Université de Bruxelles: Éditions de l’Université de Bruxelles Bruxelles · Zbl 0890.90037 [5] Goovaerts, M.; Kaas, R.; van Heerwaerden, A.; Bauwelinckx, T., Effective Actuarial Methods (1990), North-Holland: North-Holland Amsterdam [6] Johnson, N. L.; Kotz, S.; Kemp, A. W., Univariate Discrete Distributions (1992), Wiley: Wiley New York · Zbl 0773.62007 [7] Lemaire, J., Bonus-Malus Systems in Automobile Insurance (1995), Kluwer Academic: Kluwer Academic Netherlands [8] Pierre-Loti-Viaud, D., Sur les ressemblances entre les lois de Poisson, binomiales et binomiales négatives mises en évidence par un modèle paramétré commun, Rev. Roumaine Math. Pures Appl., 48, 2, 205-210 (2003) · Zbl 1047.60009 [9] D. Pierre-Loti-Viaud, Mélanges de lois sur \(\mathbb{N} \); D. Pierre-Loti-Viaud, Mélanges de lois sur \(\mathbb{N} \) [10] Walhin, J. F.; Paris, J., Using mixed Poisson processes in connexion with bonus-malus systems, ASTIN Bulletin, 29, 81-99 (1999) · Zbl 1162.91444 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.