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Time-varying credibility for frequency risk models: Estimation and tests for autoregressive specifications on the random effects

Author

Listed:
  • Jean Pinquet

    (CECO - Laboratoire d'économétrie de l'École polytechnique - X - École polytechnique - IP Paris - Institut Polytechnique de Paris - CNRS - Centre National de la Recherche Scientifique)

  • Guillén Montserrat

    (CECO - Laboratoire d'économétrie de l'École polytechnique - X - École polytechnique - IP Paris - Institut Polytechnique de Paris - CNRS - Centre National de la Recherche Scientifique)

  • Catalina Bolancé

    (UB - Universitat de Barcelona)

Abstract

This paper estimates and tests autoregressive specifications for dynamic random effects in a frequency risk model. Linear credibility predictors are derived from the estimators. Examples are provided from the automobile portfolio of a Spanish insurance company.

Suggested Citation

  • Jean Pinquet & Guillén Montserrat & Catalina Bolancé, 2003. "Time-varying credibility for frequency risk models: Estimation and tests for autoregressive specifications on the random effects," Post-Print hal-00397271, HAL.
    • Handle: RePEc:hal:journl:hal-00397271
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    References listed on IDEAS

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    1. Frees, Edward W. & Young, Virginia R. & Luo, Yu, 1999. "A longitudinal data analysis interpretation of credibility models," Insurance: Mathematics and Economics, Elsevier, vol. 24(3), pages 229-247, May.
    2. Sundt, Bjorn, 1988. "Credibility estimators with geometric weights," Insurance: Mathematics and Economics, Elsevier, vol. 7(2), pages 113-122, April.
    3. Pinquet, Jean & Guillén, Montserrat & Bolancé, Catalina, 2001. "Allowance for the Age of Claims in Bonus-Malus Systems," ASTIN Bulletin, Cambridge University Press, vol. 31(2), pages 337-348, November.
    4. Besson, Par Jean-Luc & Partrat, et Christian, 1992. "Trend et systèmes de Bonus-Malus1," ASTIN Bulletin, Cambridge University Press, vol. 22(1), pages 11-31, May.
    5. Purcaru, Oana & Denuit, Michel, 2003. "Dependence in Dynamic Claim Frequency Credibility Models," ASTIN Bulletin, Cambridge University Press, vol. 33(1), pages 23-40, May.
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    Cited by:

    1. Wei Wang & Limin Wen & Zhixin Yang & Quan Yuan, 2020. "Quantile Credibility Models with Common Effects," Risks, MDPI, vol. 8(4), pages 1-10, September.
    2. Bolancé, Catalina & Guillén, Montserrat & Pinquet, Jean, 2008. "On the link between credibility and frequency premium," Insurance: Mathematics and Economics, Elsevier, vol. 43(2), pages 209-213, October.
    3. 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.
    4. Yang Lu, 2018. "Dynamic Frailty Count Process in Insurance: A Unified Framework for Estimation, Pricing, and Forecasting," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 85(4), pages 1083-1102, December.
    5. Bermúdez i Morata, Lluís, 2009. "A priori ratemaking using bivariate Poisson regression models," Insurance: Mathematics and Economics, Elsevier, vol. 44(1), pages 135-141, February.
    6. Youn Ahn, Jae & Jeong, Himchan & Lu, Yang, 2021. "On the ordering of credibility factors," Insurance: Mathematics and Economics, Elsevier, vol. 101(PB), pages 626-638.
    7. Araichi, Sawssen & Peretti, Christian de & Belkacem, Lotfi, 2016. "Solvency capital requirement for a temporal dependent losses in insurance," Economic Modelling, Elsevier, vol. 58(C), pages 588-598.
    8. Katrien Antonio & Emiliano Valdez, 2012. "Statistical concepts of a priori and a posteriori risk classification in insurance," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 96(2), pages 187-224, June.
    9. Lluis Bermúdez i Morata, 2008. "A priori ratemaking using bivariate poisson regression models," Working Papers XREAP2008-09, Xarxa de Referència en Economia Aplicada (XREAP), revised Jul 2008.
    10. Dionne, Georges & Michaud, Pierre-Carl & Pinquet, Jean, 2013. "A review of recent theoretical and empirical analyses of asymmetric information in road safety and automobile insurance," Research in Transportation Economics, Elsevier, vol. 43(1), pages 85-97.
    11. Jean Pinquet, 2012. "Experience rating in non-life insurance," Working Papers hal-00677100, HAL.
    12. Qiang Zhang & Lijun Wu & Qianqian Cui, 2017. "The balanced credibility estimators with correlation risk and inflation factor," Statistical Papers, Springer, vol. 58(3), pages 659-672, September.
    13. Pinquet, Jean, 2020. "Positivity properties of the ARFIMA(0,d,0) specifications and credibility analysis of frequency risks," Insurance: Mathematics and Economics, Elsevier, vol. 95(C), pages 159-165.
    14. Lo, Chi Ho & Fung, Wing Kam & Zhu, Zhong Yi, 2006. "Generalized estimating equations for variance and covariance parameters in regression credibility models," Insurance: Mathematics and Economics, Elsevier, vol. 39(1), pages 99-113, August.
    15. Bermúdez, Lluís & Karlis, Dimitris, 2011. "Bayesian multivariate Poisson models for insurance ratemaking," Insurance: Mathematics and Economics, Elsevier, vol. 48(2), pages 226-236, March.
    16. Lluís Bermúdez & Dimitris Karlis & Isabel Morillo, 2020. "Modelling Unobserved Heterogeneity in Claim Counts Using Finite Mixture Models," Risks, MDPI, vol. 8(1), pages 1-13, January.
    17. Ramon Alemany & Catalina Bolance & Montserrat Guillen, 2014. "Accounting for severity of risk when pricing insurance products," Working Papers 2014-05, Universitat de Barcelona, UB Riskcenter.
    18. Zhao, Xiaobing & Zhou, Xian, 2012. "Copula models for insurance claim numbers with excess zeros and time-dependence," Insurance: Mathematics and Economics, Elsevier, vol. 50(1), pages 191-199.
    19. Shi, Peng & Valdez, Emiliano A., 2011. "A copula approach to test asymmetric information with applications to predictive modeling," Insurance: Mathematics and Economics, Elsevier, vol. 49(2), pages 226-239, September.
    20. Wen, Limin & Wu, Xianyi & Zhou, Xian, 2009. "The credibility premiums for models with dependence induced by common effects," Insurance: Mathematics and Economics, Elsevier, vol. 44(1), pages 19-25, February.
    21. Tan, Chong It, 2016. "Varying transition rules in bonus–malus systems: From rules specification to determination of optimal relativities," Insurance: Mathematics and Economics, Elsevier, vol. 68(C), pages 134-140.

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