Optimal bonus-malus systems using finite mixture models

George Tzougas, Spyridon Vrontos, Nicholas Frangos*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

26 Citations (Scopus)


This paper presents the design of optimal Bonus-Malus Systems using finite mixture models, extending the work of Lemaire (1995; Lemaire, J. (1995) Bonus-Malus Systems in Automobile Insurance. Norwell, MA: Kluwer) and Frangos and Vrontos (2001; Frangos, N. and Vrontos, S. (2001) Design of optimal bonus-malus systems with a frequency and a severity component on an individual basis in automobile insurance. ASTIN Bulletin, 31(1), 1-22). Specifically, for the frequency component we employ finite Poisson, Delaporte and Negative Binomial mixtures, while for the severity component we employ finite Exponential, Gamma, Weibull and Generalized Beta Type II mixtures, updating the posterior probability. We also consider the case of a finite Negative Binomial mixture and a finite Pareto mixture updating the posterior mean. The generalized Bonus-Malus Systems we propose, integrate risk classification and experience rating by taking into account both the a priori and a posteriori characteristics of each policyholder.

Original languageEnglish
Pages (from-to)417-444
Number of pages28
JournalASTIN Bulletin
Issue number2
Publication statusPublished - May 2014


  • a posteriori classification criteria
  • a priori classification criteria
  • claim frequency
  • claim severity
  • mixtures of distributions
  • Optimal BMS

ASJC Scopus subject areas

  • Accounting
  • Finance
  • Economics and Econometrics


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