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

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  • Bolance, Catalina
  • Guillen, Montserrat
  • Pinquet, Jean

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.
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Suggested Citation

  • Bolance, Catalina & Guillen, Montserrat & Pinquet, Jean, 2003. "Time-varying credibility for frequency risk models: estimation and tests for autoregressive specifications on the random effects," Insurance: Mathematics and Economics, Elsevier, vol. 33(2), pages 273-282, October.
  • Handle: RePEc:eee:insuma:v:33:y:2003:i:2:p:273-282
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    References listed on IDEAS

    as
    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: The Journal of the International Actuarial Association, Cambridge University Press, vol. 31(02), pages 337-348, November.
    4. Besson, Par Jean-Luc & Partrat, et Christian, 1992. "Trend et systèmes de Bonus-Malus," ASTIN Bulletin: The Journal of the International Actuarial Association, Cambridge University Press, vol. 22(01), pages 11-31, May.
    5. Purcaru, Oana & Denuit, Michel, 2003. "Dependence in Dynamic Claim Frequency Credibility Models," ASTIN Bulletin: The Journal of the International Actuarial Association, Cambridge University Press, vol. 33(01), pages 23-40, May.
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    Citations

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    Cited by:

    1. 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.
    2. repec:spr:stpapr:v:58:y:2017:i:3:d:10.1007_s00362-015-0719-6 is not listed on IDEAS
    3. 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.
    4. 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.
    5. 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.
    6. 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.
    7. 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.
    8. repec:eee:csdana:v:56:y:2012:i:12:p:3988-3999 is not listed on IDEAS
    9. 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.
    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. Bermúdez, Lluís & Karlis, Dimitris, 2011. "Bayesian multivariate Poisson models for insurance ratemaking," Insurance: Mathematics and Economics, Elsevier, vol. 48(2), pages 226-236, March.
    12. 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.
    13. 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.
    14. 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.
    15. 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.
    16. Jean Pinquet, 2012. "Experience rating in non-life insurance," Working Papers hal-00677100, HAL.

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