European Journal of Business Science and Technology 2022, 8(1):5-18 | DOI: 10.11118/ejobsat.2022.002

Multivariate Modelling of Motor Third Party Liability Insurance Claims

Aivars Spilbergs1, Andris Fomins1, Māris Krastiņ¹1
1 BA School of Business and Finance, Riga, Latvia

The aim of the study is to identity the main factors that affect claims amount paid by insurers in case of road accidents and to predict losses from valid third-party liability insurance (MTPLI) policies until their expiration. Such an assessment is essential to adequately cover MTPLI policies and ensure the sustainable development of insurance companies. The geography of the study covers the MTPLI market of Europe in the main areas, but a deeper analysis of the impact of various factors, interactions, and interrelationships in MTPLI product is focused on Latvian market data due to availability of high-quality primary data. The research is based on the analysis of primary Latvian MTPLI policies data of more than 128,000 road traffic accidents that have occurred during the time period from 2014 till 2020. Risk driver selection was performed based on the existing scientific studies and correlation analysis of the sample set. Both linear and nonlinear forms of relationships were used for modelling. A multivariate modeling was used to identify significant risk factors and to quantify their impact on loss of incidents. Statistical stability of the models was tested using chi-squared, t-tests and p-values. Validation of models calibrated where done using prediction errors measurements: mean square error (MSE), root mean squared error (RMSE), and mean absolute error (MAE) assessment both within sample and out of sample technics. The results indicated that the driver’s behavior (penalties and Bonus-Malus) as well as vehicle parameters (weight and age), had significant impacts on crash losses.

Keywords: road traffic accidents, risk drivers, non-life insurance, MTPL insurance, private insurance, passenger cars, Bonus-Malus system, MTPL insurance claims paid, multivariate modelling
JEL classification: C38, G22

Received: October 7, 2021; Revised: March 31, 2022; Accepted: April 11, 2022; Published: July 31, 2022  Show citation

ACS AIP APA ASA Harvard Chicago IEEE ISO690 MLA NLM Turabian Vancouver
Spilbergs, A., Fomins, A., & Krastiņ¹, M. (2022). Multivariate Modelling of Motor Third Party Liability Insurance Claims. European Journal of Business Science and Technology8(1), 5-18. doi: 10.11118/ejobsat.2022.002
Download citation

References

  1. Adanu, E. K., Smith, R., Powell, L. & Jones, S. 2017. Multilevel Analysis of the Role of Human Factors in Regional Disparities in Crash Outcomes. Accident Analysis and Prevention, 109, 10-17. DOI: 10.1016/j.aap.2017.09.022. Go to original source...
  2. Agresti, A. 2015. Foundations of Linear and Generalized Linear Models. Wiley & Sons. ISBN 978-1-118-73003-4.
  3. Akaike, H. 1974. A New Look at the Statistical Model Identification. IEEE Transactions on Automatic Control, 19 (6), 716-723. DOI: 10.1109/TAC.1974.1100705. Go to original source...
  4. Ayuso, M., Guillén, M. & Alcañiz, M. 2010. The Impact of Traffic Violations on the Estimated Cost of Traffic Accidents with Victims. Accident Analysis and Prevention, 42 (2), 709-717. DOI: 10.1016/j.aap.2009.10.020. Go to original source...
  5. Charpentier, A., David, A. & Elie, R. 2016. Optimal Claiming Strategies in Bonus Malus Systems and Implied Markov Chains [online]. Available at: https://ssrn.com/abstract=2790583. DOI: 10.2139/ssrn.2790583. Go to original source...
  6. de Jong, P. & Heller, G. Z. 2008. Generalized Linear Models for Insurance Data. Cambridge University Press. ISBN 978-0-521-87914-9. Go to original source...
  7. Denuit, M. & Lang, S. 2004. Non-Life Rate-Making with Bayesian GAMs. Insurance: Mathematics and Economics, 35 (3), 627-647. DOI: 10.1016/j.insmatheco.2004.08.001. Go to original source...
  8. El Kassimi, F. & Zahi, J. 2021. Non-Life Insurance Ratemaking Techniques: A Literature Review of the Classic Methods. International Journal of Accounting, Finance, Auditing, Management and Economics, 2 (1), 344-361. DOI: 10.5281/zenodo.4474479. Go to original source...
  9. Eurostat. 2021. Road Accident Fatalities - Statistics by Type of Vehicle [online]. Brussels. Available at: https://ec.europa.eu/eurostat/statistics-explained/index.php?title=Road_accident_fatalities_-_statistics_by_type_of_vehicle.
  10. FKTK. 2021. Statistics - Insurance [online]. Riga. Available at: https://www.fktk.lv/en/statistics/insurance/.
  11. Frangos, N. & Karlis, D. 2004. Modelling Losses Using an Exponential-Inverse Gaussian Distribution. Insurance: Mathematics and Economics, 35 (1), 53-67. DOI: 10.1016/j.insmatheco.2004.04.005. Go to original source...
  12. Frees, E. W. & Valdez, E. A. 2008. Hierarchical Insurance Claims Modeling. Journal of the American Statistical Association, 103 (484), 1457-1469. DOI: 10.1198/016214508000000823. Go to original source...
  13. Frees, E. W. 2010. Regression Modeling with Actuarial and Financial Applications. Cambridge University Press. ISBN 978-0-521-76011-9.
  14. Haberman, S. & Renshaw, A. E. 1996. Generalized Linear Models and Actuarial Science. Journal of the Royal Statistical Society: Series D (The Statistician), 45 (4), 407-436. DOI: 10.2307/2988543. Go to original source...
  15. Hosmer, D. W., Lemeshow, S. & Sturdivant, R. X. 2013. Applied Logistic Regression. 3rd ed. John Wiley & Sons. DOI: 10.1002/9781118548387. Go to original source...
  16. Insurance Europe. 2021. European Insurance: Preliminary Figures 2020 [online]. Brussels. Available at: https://www.insuranceeurope.eu/news.
  17. Kaas, R., Goovaerts, M., Dhaene, J. & Denuit, M. 2008. Modern Actuarial Risk Theory: Using R. 2nd ed. Springer. ISBN 978-3-540-70992-3. DOI: 10.1007/978-3-540-70998-5. Go to original source...
  18. Klein, N., Denuit, M., Lang, S. & Kneib, T. 2014. Nonlife Ratemaking and Risk Management with Bayesian Generalized Additive Models for Location, Scale, and Shape. Insurance Mathematics and Economics, 55 (C), 225-249. DOI: 10.1016/j.insmatheco.2014.02.001. Go to original source...
  19. National Safety Council. 2022. Age of Driver [online]. Available at: https://injuryfacts.nsc.org/motor-vehicle/overview/age-of-driver/.
  20. Oh, R., Kim, J. H. T. & Ahn, J. Y. 2020. Designing a Bonus-Malus System Reflecting the Claim Size Under the Dependent Frequency-Severity Model. Probability in the Engineering and Informational Sciences, 1-25. DOI: 10.1017/S0269964821000188. Go to original source...
  21. Pratama, A. S., Nurrohmah, S. & Novita, M. 2020. Determination of Net Premium Rates on Bonus-Malus System Based on Frequency and Severity Distribution. Journal of Physics: Conference Series, 1442, 012034. DOI: 10.1088/1742-6596/1442/1/012034. Go to original source...
  22. R Core Team. 2021. R: A Language and Environment for Statistical Computing [online]. Foundation for Statistical Computing, Vienna, Austria. Available at: https://www.R-project.org/.
  23. Refaeilzadeh, P., Tang, L. & Liu, H. 2016. Cross-Validation. In Liu, L. & Özsu, M. T. (eds.). Encyclopedia of Database Systems. Springer, New York, NY. DOI: 10.1007/978-1-4899-7993-3_565-2. Go to original source...
  24. Schwarz, G. 1978. Estimating the Dimension of a Model. The Annals of Statistics, 6 (2), 461-464. Go to original source...
  25. Szymañska, A. 2017. The Application of Bühlmann-Straub Model to the Estimation of the Net Premium Rate Depending on the Age of the Insured in the Motor Third Liability Insurance. Statistics in Transition New Series, 18 (1), 151-165. DOI: 10.21307/stattrans-2016-063. Go to original source...
  26. ©oltés, E., Zelinová, S. & Bilîková, M. 2019. General Linear Model: An Effective Tool for Analysis of Claim Severity in Motor Third Party Liability Insurance. Statistics in Transition New Series, 20 (4), 13-31. DOI: 10.21307/stattrans-2019-032. Go to original source...
  27. World Health Organization. 2021. Road Traffic Injuries [online]. Available at: https://www.who.int/news-room/fact-sheets/detail/road-traffic-injuries.
  28. Yunos, Z. M., Shamsuddin, S. M., Sallehuddin, R. & Alwee, R. 2019. Hybrid Predictive Modelling for Motor Insurance Claim. IOP Conference Series: Materials Science and Engineering, 551, 012075. DOI: 10.1088/1757-899X/551/1/012075. Go to original source...

This is an open access article distributed under the terms of the Creative Commons Attribution-ShareAlike 4.0 International License (CC BY-SA 4.0), which permits use, distribution, and reproduction in any medium, provided the original publication is properly cited. No use, distribution or reproduction is permitted which does not comply with these terms.