| Peer-Reviewed

Modelling a Pay-As-You-Drive Insurance Pricing Structure Using a Generalized Linear Model: Case Study of a Company in Kiambu

Received: 28 September 2015     Accepted: 15 October 2015     Published: 30 October 2015
Views:       Downloads:
Abstract

The current fixed car-year pricing of auto insurance is inefficient and actuarially inaccurate since motorists in the same risk class pay the same amount of premium regardless of the number of miles covered by the different vehicles. In this paper, a simple alternative, the pay as you drive insurance, was proposed whereby motorists only pay for the mileage covered by their vehicles. The main objective was to find a suitable probability distribution that would be used to model the per kilometer risk premiums for the total aggregate claims cost. A case study was done for a company in Kiambu county. The data collected consisted of 5 variables in 194 categories whereby the total aggregate claims cost was the dependent variable. The data collection technique was via a census. The most appropriate model was found to be the zero inflated negative binomial model. The significant factors were found to be the make of the vehicle, annual mileage, and present value of the vehicle. In addition to this, mileage was also found to be positively correlated to the total aggregate claims cost.

Published in American Journal of Theoretical and Applied Statistics (Volume 4, Issue 6)
DOI 10.11648/j.ajtas.20150406.23
Page(s) 527-533
Creative Commons

This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.

Copyright

Copyright © The Author(s), 2015. Published by Science Publishing Group

Keywords

Pay As You Drive, Generalized Linear Model, Risk Premium, Vehicle Insurance, Total Claims Cost, Correlation, Premium Pricing

References
[1] A. Nandeshwar, “Studying Auto Insurance Data,” unpublished, 2010.
[2] D. Deng and S. Paul, “Score Tests for Zero-Inflation and Over-dispersion in Generalized Linear Models,” Statistica Sinica, pp. 257-276, 2005.
[3] E. Ohlsson, and B. Johansson, “Non-Life Insurance Pricing with Generalized Linear Models,” Springer-Verlag, Berlin, 2015.
[4] H. Lennon, “Generalized Linear Models and their Extensions for Insurance Data,” unpublished, 2011.
[5] J. Bordoff and P. Noel, “The Impact of Pay As You Drive Auto Insurance in California,” Brookings Institution, 2008.
[6] J. Ferreira and E. Minikel, “Pay-As-You-Drive Auto Insurance in Massachusetts: A Risk Assessment and Report on Consumer, Industry and Environmental Benefits,” Saint Paul (MI): Department of Urban Studies and Planning, Massachusetts Institute of Technology, 2010.
[7] J. A. Nelder and R. W. M. Wedderburn, “Generalized Linear Models,” Journal of the Royal Statistical Society, A. 135, 370-384, 1972.
[8] J. Boucher, A. Pérez-Marín and M. Santolino, “Pay-As-You-Drive Insurance: The Effect of the Kilometers on the Risk of Accident,” Anales del Instituto de Acturios Espanioles, 3ª Época, 19, 135-154, 2013.
[9] M. A. Oyugi, Actuarial modeling for insurance claim severity in motor comprehensive policy using industrial statistical distributions, International Congress of Actuaries, Capetown, 2010.
[10] M. Ayuso, M. Guillén and A. M. Pérez-Marín, “ime and distance to first accident and driving patterns of young drivers with pay-as-you-drive insurance,” Accident Analysis and Prevention, 125-131, 2014.
[11] M. David, and D. V. Jemna, “Modeling the Frequency of Auto Insurance Claims by Means of Poisson and Negative Binomial Models”, Annals of the Alexandru Ioan Cuza University-Economics, 62(2), 151-168, 2015.
[12] M. David, "Automobile insurance pricing with Generalized Linear Models," Proceedings in GV-Global Virtual Conference, 2015.
[13] S. Husnjak, D. Peraković, I. Forenbacher, & M. Mumdziev, “Telematics System in Usage Based Motor Insurance,” Procedia Engineering, 100, 816-825, 2015.
[14] S. Kafkova, and L. Krivankova, “Generalized linear models in vehicle insurance,” Acta Universitatis Agriculturae et Silviculturae Mendelianae Brunensis, 62, No. 2, 383-388, 2014.
[15] T. Litman and R. Meyer, “Pay As-You-Drive Vehicle Insurance in British Columbia,” Pacific Institute for Climate Solutions, University of Victoria, 2011.
[16] T. Störmer, "Optimizing insurance pricing by incorporating consumers’ perceptions of risk classification." Zeitschrift für die gesamte Versicherungswissenschaft 104.1, 11-37, 2015.
[17] P. Jong, G. Z. Heller, “Generalized Linear Models for Insurance Data,” International Series on Actuarial Science, Cambridge University Press, 2008.
[18] Q. Vuong, “Likelihood Ratio Test form Model Selection and Non-nested hypotheses,” Econometrica: Journal of the Econometric s=Society, 307-333, 1989.
Cite This Article
  • APA Style

    Charity Mkajuma Wamwea, Benjamin Kyalo Muema, Joseph Kyalo Mung’atu. (2015). Modelling a Pay-As-You-Drive Insurance Pricing Structure Using a Generalized Linear Model: Case Study of a Company in Kiambu. American Journal of Theoretical and Applied Statistics, 4(6), 527-533. https://doi.org/10.11648/j.ajtas.20150406.23

    Copy | Download

    ACS Style

    Charity Mkajuma Wamwea; Benjamin Kyalo Muema; Joseph Kyalo Mung’atu. Modelling a Pay-As-You-Drive Insurance Pricing Structure Using a Generalized Linear Model: Case Study of a Company in Kiambu. Am. J. Theor. Appl. Stat. 2015, 4(6), 527-533. doi: 10.11648/j.ajtas.20150406.23

    Copy | Download

    AMA Style

    Charity Mkajuma Wamwea, Benjamin Kyalo Muema, Joseph Kyalo Mung’atu. Modelling a Pay-As-You-Drive Insurance Pricing Structure Using a Generalized Linear Model: Case Study of a Company in Kiambu. Am J Theor Appl Stat. 2015;4(6):527-533. doi: 10.11648/j.ajtas.20150406.23

    Copy | Download

  • @article{10.11648/j.ajtas.20150406.23,
      author = {Charity Mkajuma Wamwea and Benjamin Kyalo Muema and Joseph Kyalo Mung’atu},
      title = {Modelling a Pay-As-You-Drive Insurance Pricing Structure Using a Generalized Linear Model: Case Study of a Company in Kiambu},
      journal = {American Journal of Theoretical and Applied Statistics},
      volume = {4},
      number = {6},
      pages = {527-533},
      doi = {10.11648/j.ajtas.20150406.23},
      url = {https://doi.org/10.11648/j.ajtas.20150406.23},
      eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajtas.20150406.23},
      abstract = {The current fixed car-year pricing of auto insurance is inefficient and actuarially inaccurate since motorists in the same risk class pay the same amount of premium regardless of the number of miles covered by the different vehicles. In this paper, a simple alternative, the pay as you drive insurance, was proposed whereby motorists only pay for the mileage covered by their vehicles. The main objective was to find a suitable probability distribution that would be used to model the per kilometer risk premiums for the total aggregate claims cost. A case study was done for a company in Kiambu county. The data collected consisted of 5 variables in 194 categories whereby the total aggregate claims cost was the dependent variable. The data collection technique was via a census. The most appropriate model was found to be the zero inflated negative binomial model. The significant factors were found to be the make of the vehicle, annual mileage, and present value of the vehicle. In addition to this, mileage was also found to be positively correlated to the total aggregate claims cost.},
     year = {2015}
    }
    

    Copy | Download

  • TY  - JOUR
    T1  - Modelling a Pay-As-You-Drive Insurance Pricing Structure Using a Generalized Linear Model: Case Study of a Company in Kiambu
    AU  - Charity Mkajuma Wamwea
    AU  - Benjamin Kyalo Muema
    AU  - Joseph Kyalo Mung’atu
    Y1  - 2015/10/30
    PY  - 2015
    N1  - https://doi.org/10.11648/j.ajtas.20150406.23
    DO  - 10.11648/j.ajtas.20150406.23
    T2  - American Journal of Theoretical and Applied Statistics
    JF  - American Journal of Theoretical and Applied Statistics
    JO  - American Journal of Theoretical and Applied Statistics
    SP  - 527
    EP  - 533
    PB  - Science Publishing Group
    SN  - 2326-9006
    UR  - https://doi.org/10.11648/j.ajtas.20150406.23
    AB  - The current fixed car-year pricing of auto insurance is inefficient and actuarially inaccurate since motorists in the same risk class pay the same amount of premium regardless of the number of miles covered by the different vehicles. In this paper, a simple alternative, the pay as you drive insurance, was proposed whereby motorists only pay for the mileage covered by their vehicles. The main objective was to find a suitable probability distribution that would be used to model the per kilometer risk premiums for the total aggregate claims cost. A case study was done for a company in Kiambu county. The data collected consisted of 5 variables in 194 categories whereby the total aggregate claims cost was the dependent variable. The data collection technique was via a census. The most appropriate model was found to be the zero inflated negative binomial model. The significant factors were found to be the make of the vehicle, annual mileage, and present value of the vehicle. In addition to this, mileage was also found to be positively correlated to the total aggregate claims cost.
    VL  - 4
    IS  - 6
    ER  - 

    Copy | Download

Author Information
  • Department of Statistics and Actuarial Sciences, Jomo Kenyatta University of Agriculture and Technology, Nairobi, Kenya

  • Department of Statistics and Actuarial Sciences, Jomo Kenyatta University of Agriculture and Technology, Nairobi, Kenya

  • Department of Statistics and Actuarial Sciences, Jomo Kenyatta University of Agriculture and Technology, Nairobi, Kenya

  • Sections