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
Volume 4, Issue 6, November 2015, Pages: 527-533
Received: Sep. 28, 2015; Accepted: Oct. 15, 2015; Published: Oct. 30, 2015
Views 4049      Downloads 143
Authors
Charity Mkajuma Wamwea, Department of Statistics and Actuarial Sciences, Jomo Kenyatta University of Agriculture and Technology, Nairobi, Kenya
Benjamin Kyalo Muema, Department of Statistics and Actuarial Sciences, Jomo Kenyatta University of Agriculture and Technology, Nairobi, Kenya
Joseph Kyalo Mung’atu, Department of Statistics and Actuarial Sciences, Jomo Kenyatta University of Agriculture and Technology, Nairobi, Kenya
Article Tools
Follow on us
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.
Keywords
Pay As You Drive, Generalized Linear Model, Risk Premium, Vehicle Insurance, Total Claims Cost, Correlation, Premium Pricing
To cite this article
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, American Journal of Theoretical and Applied Statistics. Vol. 4, No. 6, 2015, pp. 527-533. doi: 10.11648/j.ajtas.20150406.23
Copyright
Copyright © 2015 Authors retain the copyright of this article.
This article is an open access article distributed under the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0/) which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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.
ADDRESS
Science Publishing Group
1 Rockefeller Plaza,
10th and 11th Floors,
New York, NY 10020
U.S.A.
Tel: (001)347-983-5186