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On the link between credibility and frequency premium

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  • Bolancé, Catalina
  • Guillén, Montserrat
  • Pinquet, Jean

Abstract

This paper questions the equidistribution assumption for the random effects in a frequency risk model. Two models are presented, which use parametric and nonparametric links between the variance of the random effect and frequency risk. They are estimated on a Spanish automobile insurance portfolio, for which a decreasing link is obtained. Conclusions are drawn for credibility and bonus-malus coefficients.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:insuma:v:43:y:2008:i:2:p:209-213
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    References listed on IDEAS

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    1. Qian, Weimin, 2000. "An application of nonparametric regression estimation in credibility theory," Insurance: Mathematics and Economics, Elsevier, vol. 27(2), pages 169-176, October.
    2. Gourieroux, Christian & Monfort, Alain & Trognon, Alain, 1984. "Pseudo Maximum Likelihood Methods: Theory," Econometrica, Econometric Society, vol. 52(3), pages 681-700, May.
    3. Harvey, A C, 1976. "Estimating Regression Models with Multiplicative Heteroscedasticity," Econometrica, Econometric Society, vol. 44(3), pages 461-465, May.
    4. Hardle, W. & Hall, P. & Ichimura, H., 1991. "Optimal smoothing in single index models," CORE Discussion Papers 1991007, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    5. 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.
    6. Hardle, Wolfgang & Linton, Oliver, 1986. "Applied nonparametric methods," Handbook of Econometrics,in: R. F. Engle & D. McFadden (ed.), Handbook of Econometrics, edition 1, volume 4, chapter 38, pages 2295-2339 Elsevier.
    7. Dufresne, François & Gerber, Hans U. & Shiu, Elias S. W., 1991. "Risk Theory with the Gamma Process," ASTIN Bulletin: The Journal of the International Actuarial Association, Cambridge University Press, vol. 21(2), pages 177-192, November.
    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. 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.
    10. Winkelmann, Rainer & Zimmermann, Klaus F., 1991. "A new approach for modeling economic count data," Economics Letters, Elsevier, vol. 37(2), pages 139-143, October.
    11. Härdle, Wolfgang & Spokoiny, V. & Sperlich, S., 1995. "Semiparametric Single Index Versus Fixed Link Function Modelling," SFB 373 Discussion Papers 1995,21, Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes.
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    Citations

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    Cited by:

    1. Ramon Alemany & Catalina Bolancé & Montserrat Guillén, 2012. "Nonparametric estimation of Value-at-Risk," Working Papers XREAP2012-19, Xarxa de Referència en Economia Aplicada (XREAP), revised Oct 2012.
    2. repec:eee:csdana:v:56:y:2012:i:12:p:3988-3999 is not listed on IDEAS
    3. repec:eee:insuma:v:85:y:2019:i:c:p:89-103 is not listed on IDEAS
    4. Jean Pinquet, 2012. "Experience rating in non-life insurance," Working Papers hal-00677100, HAL.
    5. Bermúdez, Lluís & Karlis, Dimitris, 2011. "Bayesian multivariate Poisson models for insurance ratemaking," Insurance: Mathematics and Economics, Elsevier, vol. 48(2), pages 226-236, March.
    6. 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.

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