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Copula models for insurance claim numbers with excess zeros and time-dependence

Author

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  • Zhao, Xiaobing
  • Zhou, Xian

Abstract

This paper develops two copula models for fitting the insurance claim numbers with excess zeros and time-dependence. The joint distribution of the claims in two successive periods is modeled by a copula with discrete or continuous marginal distributions. The first model fits two successive claims by a bivariate copula with discrete marginal distributions. In the second model, a copula is used to model the random effects of the conjoint numbers of successive claims with continuous marginal distributions. Zero-inflated phenomenon is taken into account in the above copula models. The maximum likelihood is applied to estimate the parameters of the discrete copula model. A two-step procedure is proposed to estimate the parameters in the second model, with the first step to estimate the marginals, followed by the second step to estimate the unobserved random effect variables and the copula parameter. Simulations are performed to assess the proposed models and methodologies.

Suggested Citation

  • 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.
  • Handle: RePEc:eee:insuma:v:50:y:2012:i:1:p:191-199
    DOI: 10.1016/j.insmatheco.2011.11.004
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    References listed on IDEAS

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    1. Chen, Xiaohong & Fan, Yanqin, 2006. "Estimation of copula-based semiparametric time series models," Journal of Econometrics, Elsevier, vol. 130(2), pages 307-335, February.
    2. Gathy, Maude & Lefèvre, Claude, 2010. "On the Lagrangian Katz family of distributions as a claim frequency model," Insurance: Mathematics and Economics, Elsevier, vol. 47(1), pages 76-83, August.
    3. repec:sae:ecolab:v:16:y:2006:i:2:p:1-2 is not listed on IDEAS
    4. Lemaire, Jean, 1977. "La Soif du Bonus," ASTIN Bulletin: The Journal of the International Actuarial Association, Cambridge University Press, vol. 9(1-2), pages 181-190, January.
    5. Bargès, Mathieu & Cossette, Hélène & Loisel, Stéphane & Marceau, Étienne, 2011. "On the Moments of Aggregate Discounted Claims with Dependence Introduced by a FGM Copula," ASTIN Bulletin: The Journal of the International Actuarial Association, Cambridge University Press, vol. 41(1), pages 215-238, May.
    6. Sundt, Bjorn, 1988. "Credibility estimators with geometric weights," Insurance: Mathematics and Economics, Elsevier, vol. 7(2), pages 113-122, April.
    7. Chiung-Yu Huang & Mei-Cheng Wang, 2004. "Joint Modeling and Estimation for Recurrent Event Processes and Failure Time Data," Journal of the American Statistical Association, American Statistical Association, vol. 99, pages 1153-1165, December.
    8. Natacha Brouhns & Montserrat Guillén & Michel Denuit & Jean Pinquet, 2003. "Bonus‐Malus Scales in Segmented Tariffs With Stochastic Migration Between Segments," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 70(4), pages 577-599, December.
    9. 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.
    10. Gómez-Déniz, Emilio & Sarabia, José María & Calderín-Ojeda, Enrique, 2011. "A new discrete distribution with actuarial applications," Insurance: Mathematics and Economics, Elsevier, vol. 48(3), pages 406-412, May.
    11. Nikolay Nenovsky & S. Statev, 2006. "Introduction," Post-Print halshs-00260898, HAL.
    12. 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.
    13. 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(1), pages 23-40, May.
    14. 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.
    15. 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.
    16. Drgabriel Escarela & Jacques Carriere, 2006. "A bivariate model of claim frequencies and severities," Journal of Applied Statistics, Taylor & Francis Journals, vol. 33(8), pages 867-883.
    17. Antonio, Katrien & Frees, Edward W. & Valdez, Emiliano A., 2010. "A Multilevel Analysis of Intercompany Claim Counts," ASTIN Bulletin: The Journal of the International Actuarial Association, Cambridge University Press, vol. 40(1), pages 151-177, May.
    18. Kaishev, Vladimir K. & Dimitrova, Dimitrina S., 2006. "Excess of loss reinsurance under joint survival optimality," Insurance: Mathematics and Economics, Elsevier, vol. 39(3), pages 376-389, December.
    19. Cossette, Hélène & Marceau, Étienne & Toureille, Florent, 2011. "Risk models based on time series for count random variables," Insurance: Mathematics and Economics, Elsevier, vol. 48(1), pages 19-28, January.
    20. Cossette, Hélène & Marceau, Etienne & Maume-Deschamps, Véronique, 2010. "Discrete-Time Risk Models Based on Time Series for Count Random Variables," ASTIN Bulletin: The Journal of the International Actuarial Association, Cambridge University Press, vol. 40(1), pages 123-150, May.
    21. Bermúdez, Lluís & Karlis, Dimitris, 2011. "Bayesian multivariate Poisson models for insurance ratemaking," Insurance: Mathematics and Economics, Elsevier, vol. 48(2), pages 226-236, March.
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