caa a22 4500 388071079 CHVBK 20180307125148.0 cr unu---uuuuu 161130e199911 xx s 000 0 eng 10.2143/AST.29.2.504619 doi S0515036100012629 pii (NATIONALLICENCE)cambridge-10.2143/AST.29.2.504619 Accounting for Individual Over-Dispersion in a Bonus-Malus Automobile Insurance System [Elektronische Daten] Individual automobile insurance claims are characterized by over-dispersion relative to the Poisson model. In addition, claim propensities vary among individuals in any insurance portfolio. This paper presents a model which takes account of both characteristics. The model employs the negative-binomial distribution as the distribution for individual-level claims and a Pareto distribution as the distribution for claim propensities within the portfolio. The paper shows that the resulting model is tractable and has a number of attractive properties which make it suitable for this application. The fit of the model to actual claim numbers for automobile third party liability insurance is examined and found acceptable. Bayes theorem is then applied to this model to calculate illustrative optimal premiums under the Bonus-Malus System (BMS). Copyright © International Actuarial Association 1999 Shengwang Meng Department of Statistics Renmin University, Beijing, China Wei Yuan Department of Statistics Renmin University, Beijing, China Whitmore G.A. Faculty of Management McGill University, Montreal, Canada ASTIN Bulletin Cambridge University Press 29/2(1999-11), 327-337 0515-0361 29:2<327 1999 29 ASB https://doi.org/10.2143/AST.29.2.504619 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.2143/AST.29.2.504619 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Shengwang Meng Department of Statistics Renmin University, Beijing, China NATIONALLICENCE 700 1- Wei Yuan Department of Statistics Renmin University, Beijing, China NATIONALLICENCE 700 1- Whitmore G.A. Faculty of Management McGill University, Montreal, Canada NATIONALLICENCE 773 0- ASTIN Bulletin Cambridge University Press 29/2(1999-11), 327-337 0515-0361 29:2<327 1999 29 ASB CC0 http://creativecommons.org/publicdomain/zero/1.0 nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-cambridge