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Hierarchical generalized linear models, correlation and a posteriori ratemaking

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  • Gning, Lucien
  • Diagne, M.L.
  • Tchuenche, J.M.

Abstract

Insurance pricing is the premium set by the insurance companies. Hierarchical generalized linear models (HGLM) particularly those dealing with count data and their application to insurance pricing are investigated. In the context of car insurance a posteriori ratemaking, the Poisson-gamma HGLM and the negative binomial-beta HGLM are compared. It is shown that contrary to the HGLM Poisson-gamma, the negative binomial-beta HGLM fits the correlation between successive claim numbers of a given insured, which generates a significant difference of the resulting a posteriori premiums. Simulations and an application based on a real portfolio of car insurance are carried out to support the theoretical results.

Suggested Citation

  • Gning, Lucien & Diagne, M.L. & Tchuenche, J.M., 2023. "Hierarchical generalized linear models, correlation and a posteriori ratemaking," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 614(C).
    • Handle: RePEc:eee:phsmap:v:614:y:2023:i:c:s0378437123000894
    DOI: 10.1016/j.physa.2023.128534
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    References listed on IDEAS

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    1. Dionne, Georges & Vanasse, Charles, 1989. "A Generalization of Automobile Insurance Rating Models: The Negative Binomial Distribution with a Regression Component," ASTIN Bulletin, Cambridge University Press, vol. 19(2), pages 199-212, November.
    2. Shi, Peng & Valdez, Emiliano A., 2014. "Multivariate negative binomial models for insurance claim counts," Insurance: Mathematics and Economics, Elsevier, vol. 55(C), pages 18-29.
    3. Molas, Marek & Lesaffre, Emmanuel, 2011. "Hierarchical Generalized Linear Models: The R Package HGLMMM," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 39(i13).
    4. Tzougas, George & Pignatelli di Cerchiara, Alice, 2021. "The multivariate mixed Negative Binomial regression model with an application to insurance a posteriori ratemaking," Insurance: Mathematics and Economics, Elsevier, vol. 101(PB), pages 602-625.
    5. Jean‐Philippe Boucher & Michel Denuit & Montserrat Guillen, 2009. "Number of Accidents or Number of Claims? An Approach with Zero‐Inflated Poisson Models for Panel Data," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 76(4), pages 821-846, December.
    6. Boucher, Jean-Philippe & Inoussa, Rofick, 2014. "A Posteriori Ratemaking With Panel Data," ASTIN Bulletin, Cambridge University Press, vol. 44(3), pages 587-612, September.
    7. Hausman, Jerry & Hall, Bronwyn H & Griliches, Zvi, 1984. "Econometric Models for Count Data with an Application to the Patents-R&D Relationship," Econometrica, Econometric Society, vol. 52(4), pages 909-938, July.
    8. Tzougas, George & Hoon, W. L. & Lim, J. M., 2019. "The negative binomial-inverse Gaussian regression model with an application to insurance ratemaking," LSE Research Online Documents on Economics 101728, London School of Economics and Political Science, LSE Library.
    9. Bermúdez, Lluís & Karlis, Dimitris, 2012. "A finite mixture of bivariate Poisson regression models with an application to insurance ratemaking," Computational Statistics & Data Analysis, Elsevier, vol. 56(12), pages 3988-3999.
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