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Quantile credibility models


  • Pitselis, Georgios


In this paper, we develop links between credibility theory and quantiles. More specifically, we show how quantiles can be embedded within the classical Bühlmann’s (1967) credibility model and within Hachemeister’s (1975) regression credibility model. The context of influence function is also incorporated into the above two models. For each model, credibility estimators are established and applications to real data are presented.

Suggested Citation

  • Pitselis, Georgios, 2013. "Quantile credibility models," Insurance: Mathematics and Economics, Elsevier, vol. 52(3), pages 477-489.
  • Handle: RePEc:eee:insuma:v:52:y:2013:i:3:p:477-489 DOI: 10.1016/j.insmatheco.2013.02.011

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    References listed on IDEAS

    1. Koenker, Roger W & Bassett, Gilbert, Jr, 1978. "Regression Quantiles," Econometrica, Econometric Society, vol. 46(1), pages 33-50, January.
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    4. Payandeh Najafabadi, Amir T., 2010. "A new approach to the credibility formula," Insurance: Mathematics and Economics, Elsevier, vol. 46(2), pages 334-338, April.
    5. Moshe Buchinsky, 1998. "Recent Advances in Quantile Regression Models: A Practical Guideline for Empirical Research," Journal of Human Resources, University of Wisconsin Press, vol. 33(1), pages 88-126.
    6. Portnoy, Esther, 1997. "Regression-quantile graduation of Australian life tables, 1946-1992," Insurance: Mathematics and Economics, Elsevier, vol. 21(2), pages 163-172, November.
    7. Koenker,Roger, 2005. "Quantile Regression," Cambridge Books, Cambridge University Press, number 9780521845731, March.
    8. Denuit, Michel, 2008. "Comonotonic approximations to quantiles of life annuity conditional expected present value," Insurance: Mathematics and Economics, Elsevier, vol. 42(2), pages 831-838, April.
    9. Kudryavtsev, Andrey A., 2009. "Using quantile regression for rate-making," Insurance: Mathematics and Economics, Elsevier, vol. 45(2), pages 296-304, October.
    10. Gebizlioglu, Omer L. & Yagci, Banu, 2008. "Tolerance intervals for quantiles of bivariate risks and risk measurement," Insurance: Mathematics and Economics, Elsevier, vol. 42(3), pages 1022-1027, June.
    11. Maritz, J. S., 1989. "Linear empirical Bayes estimation of quantiles," Statistics & Probability Letters, Elsevier, vol. 8(1), pages 59-65, May.
    12. De Vylder, Fl., 1978. "Parameter Estimation in Credibility Theory," ASTIN Bulletin: The Journal of the International Actuarial Association, Cambridge University Press, vol. 10(01), pages 99-112, May.
    13. Pitt, D. G. W., 2006. "Regression Quantile Analysis of Claim Termination Rates for Income Protection Insurance," Annals of Actuarial Science, Cambridge University Press, vol. 1(02), pages 345-357, September.
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    Cited by:

    1. repec:eee:insuma:v:74:y:2017:i:c:p:122-134 is not listed on IDEAS
    2. Pitselis, Georgios, 2016. "Credible risk measures with applications in actuarial sciences and finance," Insurance: Mathematics and Economics, Elsevier, vol. 70(C), pages 373-386.


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