Using mixed poisson processes in connection with bonus-malus systems

ASTIN Bulletin

Volumn 29, Issue 1, 1999, Pages 81-99

  Walhin, J F ^a,b   Paris, J ^a  

^a UNIVERSITÉ CATHOLIQUE DE LOUVAIN   (Belgium)

^b Le Mans Assurances   (Belgium)

Author keywords

Bayes theorem; bonus malus systems; Hofmann's distribution; Mixed Poisson processes; non parametric estimation; stationary distribution

Indexed keywords

EID: 4344585241     PISSN: 05150361     EISSN: 17831350     Source Type: Journal    
DOI: 10.2143/AST.29.1.504607     Document Type: Article

References (16)

1. Bühlmann, H. (1970). Mathematical Models in Risk Theory. Springer-Verlag, Berlin.
2. Coene, G. and Doray, L.G. (1996). A Financially Balanced Bonus-Malus System. ASTIN Bulletin, 26: 107–115.
3. Dufresne, F. (1988). Distributions Stationnaires d'un Système Bonus-Malus et Probabilité de Ruine. ASTIN Bulletin, 18: 31–46.
4. Dufresne, F. (1995). The Efficiency of the Swiss Bonus-Malus System. Bulletin of the Swiss Actuaries, 1995(1): 29–41.
5. Feller, W. (1971). An introduction to Probability Theory and its Applications Vol II (3ed). Wiley, New York.
6. Geller, H. (1979). An introduction to Mathematical Risk Theory. University of Pennsylvania.
7. Hofmann, M. (1955). Uber zusammengesetzte poisson-prozesse und ihre Anwendungen in der Unfall versicherung. Bulletin of the Swiss Actuaries, 55: 499–575.
8. Hürlimann, W. (1990). On Maximum Likelihood Estimation for Count Data Models. Insurance: Mathematics and Economics, 9: 39–49.
9. Kestemont, R.M. and Paris, J. (1985). Sur l'Ajustement du Nombre de Sinistres. Bulletin of the Swiss Actuaries, 85: 157–164.
10. Lemaire, J. (1985). Automobile Insurance: Actuarial Models. Kluwer-Nijhoff, Netherlands.
11. Lindsay, B. (1995). Mixture Models: Theory, Geometry and Applications. Pennsylvania State University.
12. Loimaranta, K. (1972). Some Asymptotic Properties of Bonus Systems. ASTIN Bulletin, 6: 233–245.
13. Maceda, E. (1948). On the Compound and Generalized Poisson Distributions. Annals of Mathematical Statistics, 19: 414–416.
14. Panjer, H.H. (1981). Recursive Evaluation of a Family of Compound Distributions. ASTIN Bulletin, 12: 22–26.
15. Simar, L. (1976). Maximum Likelihood Estimation of a Compound Poisson Process. The Annals of Statistics, 4: 1200–1209.
16. Tremblay, L. (1992). Using the Poisson Inverse Gaussian Distribution in Bonus-Malus Systems. ASTIN Bulletin, 22: 97–106.