Hostname: page-component-586b7cd67f-dsjbd Total loading time: 0 Render date: 2024-11-30T16:55:36.277Z Has data issue: false hasContentIssue false
  • English
  • Français

PREDICTIVE CLAIM SCORES FOR DYNAMIC MULTI-PRODUCT RISK CLASSIFICATION IN INSURANCE

Published online by Cambridge University Press:  04 November 2020

Robert Matthijs Verschuren Open the ORCID record for Robert Matthijs Verschuren [Opens in a new window]
Robert Matthijs Verschuren*
Affiliation:
Amsterdam School of Economics University of Amsterdam Roetersstraat 11, 1018 WB, Amsterdam The Netherlands E-Mail: [email protected]
*
E-Mail: [email protected]
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

It has become standard practice in the non-life insurance industry to employ generalized linear models (GLMs) for insurance pricing. However, these GLMs traditionally work only with a priori characteristics of policyholders, while nowadays we increasingly have a posteriori information of individual customers available across multiple product categories. In this paper, we therefore develop a framework to capture this a posteriori information over several product lines using a dynamic claim score. More specifically, we extend the bonus-malus-panel model of Boucher and Inoussa (2014) and Boucher and Pigeon (2018) to include claim scores from other product categories and to allow for nonlinear effects of these scores. The application of the proposed multi-product framework to a Dutch property and casualty insurance portfolio shows that customers’ individual claims experience can have a significant impact on the risk classification. Moreover, it indicates that considerably more profits can be gained by accounting for their multi-product claims experience.

Keywords

Multi-product risk profilesdynamic claim scorebonus-malus systemsgeneralized additive modelscross-selling potentialinsurance pricingC23C52G22
Type
Research Article
Information
ASTIN Bulletin: The Journal of the IAA , Volume 51 , Issue 1 , January 2021 , pp. 1 - 25
Creative Commons
Creative Common License - CCCreative Common License - BY
This is an Open Access article, distributed under the terms of the Creative Commons Attribution licence (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted re-use, distribution, and reproduction in any medium, provided the original work is properly cited.
Copyright
© 2020 by Astin Bulletin. All rights reserved

References

Antonio, K. and Valdez, E.A. (2012) Statistical concepts of a priori and a posteriori risk classification in insurance. AStA Advances in Statistical Analysis, 96(2), 187–224.CrossRefGoogle Scholar
Barseghyan, L., Molinari, F., Morris, D.S. and Teitelbaum, J.C. (2020) The cost of legal restrictions on experience rating. Journal of Empirical Legal Studies, 17(1), 38–70.CrossRefGoogle Scholar
Bermúdez, L., Guillén, M. and Karlis, D. (2018) Allowing for time and cross dependence assumptions between claim counts in ratemaking models. Insurance: Mathematics and Economics, 83, 161–169.Google Scholar
Bermúdez, L. and Karlis, D. (2011) Bayesian multivariate Poisson models for insurance ratemaking. Insurance: Mathematics and Economics, 48(2), 226–236.Google Scholar
Boucher, J.-P. and Inoussa, R. (2014) A posteriori ratemaking with panel data. ASTIN Bulletin, 44(3), 587–612.CrossRefGoogle Scholar
Boucher, J.-P. and Pigeon, M. (2018) A claim score for dynamic claim counts modeling. Working Paper, December 2018. Available online at https://arxiv.org/abs/1812.06157.Google Scholar
Czado, C., Kastenmeier, R., Brechmann, E.C. and Min, A. (2012) A mixed copula model for insurance claims and claim sizes. Scandinavian Actuarial Journal, 2012(4), 278–305.CrossRefGoogle Scholar
Denuit, M., Maréchal, X., Pitrebois, S. and Walhin, J.-F. (2007) Actuarial Modelling of Claim Counts: Risk Classification, Credibility and Bonus-Malus Systems. New York: Wiley.CrossRefGoogle Scholar
Englund, M., Guillén, M., Gustafsson, J., Nielsen, L.H. and Nielsen, J.P. (2008) Multivariate latent risk: A credibility approach. ASTIN Bulletin, 38(1), 137–146.CrossRefGoogle Scholar
Englund, M., Gustafsson, J., Nielsen, J.P. and Thuring, F. (2009) Multidimensional credibility with time effects: An application to commercial business lines. The Journal of Risk and Insurance, 76(2), 443–453.CrossRefGoogle Scholar
Frees, E.W., Meyers, G. and Cummings, A.D. (2011) Summarizing insurance scores using a Gini index. Journal of the American Statistical Association, 106(495), 1085–1098.CrossRefGoogle Scholar
Frees, E.W., Meyers, G. and Cummings, A.D. (2014) Insurance ratemaking and a Gini index. The Journal of Risk and Insurance, 81(2), 335–366.CrossRefGoogle Scholar
Garrido, J., Genest, C. and Schulz, J. (2016) Generalized linear models for dependent frequency and severity of insurance claims. Insurance: Mathematics and Economics, 70, 205–215.Google Scholar
Gini, C. (1912) Variabilità e Mutabilità Contributo allo Studio delle Distribuzioni e delle Relazioni Statistiche. Bologna: Cuppini.Google Scholar
Haberman, S. and Renshaw, A.E. (1996) Generalized linear models and actuarial science. Journal of the Royal Statistical Society. Series D (The Statistician), 45(4), 407–436.Google Scholar
Hastie, T. and Tibshirani, R. (1986) Generalized additive models. Statistical Science, 1(3), 297–310.CrossRefGoogle Scholar
Hastie, T., Tibshirani, R. and Friedman, J. (2009) The Elements of Statistical Learning: Data Mining, Inference, and Prediction. New York: Springer.CrossRefGoogle Scholar
Henckaerts, R., Antonio, K., Clijsters, M. and Verbelen, R. (2018) A data driven binning strategy for the construction of insurance tariff classes. Scandinavian Actuarial Journal, 2018(8), 681–705.CrossRefGoogle Scholar
Henckaerts, R., Côté, M.-P., Antonio, K. and Verbelen, R. (2020) Boosting insights in insurance tariff plans with tree-based machine learning methods. North American Actuarial Journal, 1–31.CrossRefGoogle Scholar
Kaas, R., Goovaerts, M., Dhaene, J. and Denuit, M. (2008) Modern Actuarial Risk Theory: Using R. Berlin, Heidelberg: Springer.CrossRefGoogle Scholar
Lemaire, J. (1998) Bonus-malus systems: The European and Asian approach to merit-rating. North American Actuarial Journal, 2(1), 26–38.CrossRefGoogle Scholar
Lorenz, M.O. (1905) Methods of measuring the concentration of wealth. Publications of the American Statistical Association, 9(70), 209–219.CrossRefGoogle Scholar
Nelder, J.A. and Wedderburn, R.W.M. (1972) Generalized linear models. Journal of the Royal Statistical Society. Series A (General), 135(3), 370–384.CrossRefGoogle Scholar
Ohlsson, E. and Johansson, B. (2010) Non-Life Insurance Pricing with Generalized Linear Models. Berlin, Heidelberg: Springer.CrossRefGoogle Scholar
Pechon, F., Trufin, J. and Denuit, M. (2018) Multivariate modelling of household claim frequencies in motor third-party liability insurance. ASTIN Bulletin, 48(3), 969–993.CrossRefGoogle Scholar
Pinquet, J. (1997) Allowance for cost of claims in bonus-malus systems. ASTIN Bulletin, 27(1), 33–57.CrossRefGoogle Scholar
Quan, Z. and Valdez, E.A. (2018) Predictive analytics of insurance claims using multivariate decision trees. Dependence Modeling, 6(1), 377–407.CrossRefGoogle Scholar
Shi, P. and Valdez, E.A. (2014) Multivariate Negative Binomial models for insurance claim counts. Insurance: Mathematics and Economics, 55(1), 18–29.Google Scholar
Tzougas, G., Vrontos, S. and Frangos, N. (2014) Optimal bonus-malus systems using finite mixture models. ASTIN Bulletin, 44(2), 417–444.CrossRefGoogle Scholar
Tzougas, G., Vrontos, S. and Frangos, N. (2018) Bonus-Malus Systems with two-component mixture models arising from different parametric families. North American Actuarial Journal, 22(1), 55–91.CrossRefGoogle Scholar
Wood, S.N. (2006) Generalized Additive Models: An Introduction with R. New York: Chapman and Hall/CRC.CrossRefGoogle Scholar
Yee, T.W. and Hastie, T.J. (2003) Reduced-rank vector generalized linear models. Statistical Modeling, 3(1), 15–41.CrossRefGoogle Scholar
Supplementary material: PDF

Verschuren supplementary material

Appendix C
Download Verschuren supplementary material(PDF)
PDF 220.9 KB
Supplementary material: File

Verschuren supplementary material

R codes
Download Verschuren supplementary material(File)
File 60 KB