European Actuarial Journal

, Volume 5, Issue 1, pp 1–10 | Cite as

The impact of covariates on a bonus–malus system: an application of Taylor’s model

Original Research Paper


Obviously, the design of a bonus–malus system has to take into consideration all rating variables used by the auto insurance carrier. For instance, a single male urban driver is likely to be penalized twice, a priori through explicit surcharges linked to his risk class, and a posteriori through premium increases triggered by the transition rules of the bonus–malus system, creating the possibility of excessive premiums through double-counting for the same reason. Taylor (ASTIN Bull 27:319–327, 1997) developed a Bayesian model to evaluate the impact of covariate rating variables on bonus–malus premium levels, but could not access actual data to implement his model. We present the first real-life application of Taylor’s research, by using a unique database originating from Taiwan and the bonus–malus system in force in this island. Our data combines car and insurance information from the leading insurer in the island with annual mileage readings from a network of repair shops operated by the largest car manufacturer—over a quarter million policy-years. Park et al. (The use of annual mileage as a rating variable. Working paper, 2014), using the same data, used negative binomial regression to prove that mileage is by far the best predictor of accidents. The application of Taylor’s model concludes that the impact of mileage on bonus–malus premium levels is small. Therefore, double-counting should not be considered as a major concern in practice.


Third-party liability auto insurance Bonus–malus systems Rating variables Annual mileage 



Sojung Park appreciates the support from the Institute of Management Research at Seoul National University.


  1. 1.
    Bailey R, Simon L (1960) Two studies in automobile insurance ratemaking. ASTIN Bull 1:192–217Google Scholar
  2. 2.
    Bair ST, Huang R, Wang K (2012) Can vehicle maintenance records predict automobile accidents? J Risk Insur 79:567–584CrossRefGoogle Scholar
  3. 3.
    Ferreira J, Minikel E (2013) Measuring per mile risk for pay-as-you-drive auto insurance. Transp Res Rec: J Transp Res Board 2297:97–103CrossRefGoogle Scholar
  4. 4.
    Johnson N, Kemp A, Kotz S (2005) Univariate discrete distributions. Wiley, New YorkMATHCrossRefGoogle Scholar
  5. 5.
    Lemaire J (1985) Automobile insurance: actuarial models. Kluwer Nijhoff Publishing, BostonCrossRefGoogle Scholar
  6. 6.
    Lemaire J, Zi H (1994) A comparative analysis of 30 bonus–malus systems. ASTIN Bull 24:287–309CrossRefGoogle Scholar
  7. 7.
    Lemaire J (1995) Bonus–malus systems in automobile insurance. Kluwer Nijhoff Publishing, BostonCrossRefGoogle Scholar
  8. 8.
    Litman T (2011) Distance-based vehicle insurance feasibility, costs and benefits. Victoria Transport Policy Inst. Accessed 2 August 2014
  9. 9.
    Park S, Lemaire J, Wang K (2014) The use of annual mileage as a rating variable. Working paperGoogle Scholar
  10. 10.
    Pitrebois S, Denuit M, Walhin J-F (2003) Setting a bonus–malus scale in the presence of other rating factors. ASTIN Bull 33:419–436MATHMathSciNetCrossRefGoogle Scholar
  11. 11.
    Taiwan Insurance Institute (2014) Insurance Laws and Regulations Database. Accessed on 3 April 2015
  12. 12.
    Taylor G (1997) Setting a bonus–malus scale in the presence of other rating factors. ASTIN Bull 27:319–327CrossRefGoogle Scholar

Copyright information

© DAV / DGVFM 2015

Authors and Affiliations

  • Jean Lemaire
    • 1
  • Sojung Carol Park
    • 2
  • Kili C. Wang
    • 3
  1. 1.Wharton SchoolUniversity of PennsylvaniaPhiladelphiaUSA
  2. 2.College of Business AdministrationSeoul National UniversitySeoulRepublic of Korea
  3. 3.Tamkang UniversityTaipeiTaiwan

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