IDEAS home Printed from https://ideas.repec.org/a/eee/insuma/v52y2013i3p477-489.html
   My bibliography  Save this article

Quantile credibility models

Author

Listed:
  • Pitselis, Georgios

Abstract

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
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0167668713000243
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.insmatheco.2013.02.011?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. 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.
    2. 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.
    3. Koenker,Roger, 2005. "Quantile Regression," Cambridge Books, Cambridge University Press, number 9780521845731.
    4. De Vylder, Fl., 1978. "Parameter Estimation in Credibility Theory," ASTIN Bulletin, Cambridge University Press, vol. 10(1), pages 99-112, May.
    5. Powell, James L., 1986. "Censored regression quantiles," Journal of Econometrics, Elsevier, vol. 32(1), pages 143-155, June.
    6. Kudryavtsev, Andrey A., 2009. "Using quantile regression for rate-making," Insurance: Mathematics and Economics, Elsevier, vol. 45(2), pages 296-304, October.
    7. 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(2), pages 345-357, September.
    8. Portnoy, Esther, 1997. "Regression-quantile graduation of Australian life tables, 1946-1992," Insurance: Mathematics and Economics, Elsevier, vol. 21(2), pages 163-172, November.
    9. 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.
    10. Maritz, J. S., 1989. "Linear empirical Bayes estimation of quantiles," Statistics & Probability Letters, Elsevier, vol. 8(1), pages 59-65, May.
    11. Payandeh Najafabadi, Amir T., 2010. "A new approach to the credibility formula," Insurance: Mathematics and Economics, Elsevier, vol. 46(2), pages 334-338, April.
    12. Koenker, Roger W & Bassett, Gilbert, Jr, 1978. "Regression Quantiles," Econometrica, Econometric Society, vol. 46(1), pages 33-50, January.
    13. Jewell, William S., 1974. "Credible Means are exact Bayesian for Exponential Families," ASTIN Bulletin, Cambridge University Press, vol. 8(1), pages 77-90, September.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Pitselis, Georgios, 2017. "Risk measures in a quantile regression credibility framework with Fama/French data applications," Insurance: Mathematics and Economics, Elsevier, vol. 74(C), pages 122-134.
    2. Cheung, Ka Chun & Yam, Sheung Chi Phillip & Zhang, Yiying, 2022. "Satisficing credibility for heterogeneous risks," European Journal of Operational Research, Elsevier, vol. 298(2), pages 752-768.
    3. Pitselis, Georgios, 2016. "Credible risk measures with applications in actuarial sciences and finance," Insurance: Mathematics and Economics, Elsevier, vol. 70(C), pages 373-386.
    4. Pitselis, Georgios, 2020. "Multi-stage nested classification credibility quantile regression model," Insurance: Mathematics and Economics, Elsevier, vol. 92(C), pages 162-176.
    5. Chen, Yongzhao & Cheung, Ka Chun & Choi, Hugo Ming Cheung & Yam, Sheung Chi Phillip, 2020. "Evolutionary credibility risk premium," Insurance: Mathematics and Economics, Elsevier, vol. 93(C), pages 216-229.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Pitselis, Georgios, 2020. "Multi-stage nested classification credibility quantile regression model," Insurance: Mathematics and Economics, Elsevier, vol. 92(C), pages 162-176.
    2. Pitselis, Georgios, 2017. "Risk measures in a quantile regression credibility framework with Fama/French data applications," Insurance: Mathematics and Economics, Elsevier, vol. 74(C), pages 122-134.
    3. Fuzi, Mohd Fadzli Mohd & Jemain, Abdul Aziz & Ismail, Noriszura, 2016. "Bayesian quantile regression model for claim count data," Insurance: Mathematics and Economics, Elsevier, vol. 66(C), pages 124-137.
    4. Halkos, George E., 2011. "Nonparametric modelling of biodiversity: Determinants of threatened species," Journal of Policy Modeling, Elsevier, vol. 33(4), pages 618-635, July.
    5. Halkos, George, 2010. "Modelling biodiversity," MPRA Paper 39075, University Library of Munich, Germany.
    6. Genya Kobayashi & Hideo Kozumi, 2012. "Bayesian analysis of quantile regression for censored dynamic panel data," Computational Statistics, Springer, vol. 27(2), pages 359-380, June.
    7. Jacob A. Bikker & Laura Spierdijk & Pieter Jelle van der Sluis, 2005. "Cheap versus Expensive Trades: Assessing the Determinants of Market Impact Costs," DNB Working Papers 069, Netherlands Central Bank, Research Department.
    8. Huber, Martin & Melly, Blaise, 2011. "Quantile Regression in the Presence of Sample Selection," Economics Working Paper Series 1109, University of St. Gallen, School of Economics and Political Science.
    9. Eric Bouye & Mark Salmon, 2009. "Dynamic copula quantile regressions and tail area dynamic dependence in Forex markets," The European Journal of Finance, Taylor & Francis Journals, vol. 15(7-8), pages 721-750.
    10. Gustavsen, Geir Waehler & Jolliffe, Dean & Rickertsen, Kyrre, 2008. "Censored Quantile Regression and Purchases of Ice Cream," 2008 Annual Meeting, July 27-29, 2008, Orlando, Florida 6534, American Agricultural Economics Association (New Name 2008: Agricultural and Applied Economics Association).
    11. Gustavsen, Geir Wæhler & Rickertsen, Kyrre, 2013. "Adjusting VAT rates to promote healthier diets in Norway: A censored quantile regression approach," Food Policy, Elsevier, vol. 42(C), pages 88-95.
    12. Pitselis, Georgios, 2016. "Credible risk measures with applications in actuarial sciences and finance," Insurance: Mathematics and Economics, Elsevier, vol. 70(C), pages 373-386.
    13. Geir Wæhler Gustavsen & Kyrre Rickertsen, 2009. "The effects of taxes on purchases of sugar-sweetened carbonated soft drinks: a quantile regression approach," Applied Economics, Taylor & Francis Journals, vol. 43(6), pages 707-716.
    14. Deborah A. Cobb-Clark & Sonja C. Kassenboehmer & Mathias G. Sinning, 2013. "Locus of Control and Savings," Ruhr Economic Papers 0455, Rheinisch-Westfälisches Institut für Wirtschaftsforschung, Ruhr-Universität Bochum, Universität Dortmund, Universität Duisburg-Essen.
    15. Parente, Paulo M.D.C. & Smith, Richard J., 2011. "Gel Methods For Nonsmooth Moment Indicators," Econometric Theory, Cambridge University Press, vol. 27(1), pages 74-113, February.
    16. Duschl, Matthias & Schimke, Antje & Brenner, Thomas & Luxen, Dennis, 2011. "Firm growth and the spatial impact of geolocated external factors: Empirical evidence for German manufacturing firms," Working Paper Series in Economics 36, Karlsruhe Institute of Technology (KIT), Department of Economics and Management.
    17. Tang, Linjun & Zhou, Zhangong & Wu, Changchun, 2012. "Weighted composite quantile estimation and variable selection method for censored regression model," Statistics & Probability Letters, Elsevier, vol. 82(3), pages 653-663.
    18. Agbeyegbe, Terence D., 2015. "An inverted U-shaped crude oil price return-implied volatility relationship," Review of Financial Economics, Elsevier, vol. 27(C), pages 28-45.
    19. Gaglianone, Wagner Piazza & Lima, Luiz Renato & Linton, Oliver & Smith, Daniel R., 2011. "Evaluating Value-at-Risk Models via Quantile Regression," Journal of Business & Economic Statistics, American Statistical Association, vol. 29(1), pages 150-160.
    20. Gustavsen, Geir Waehler, 2005. "Public Policies and the Demand for Carbonated Soft Drinks: A Censored Quantile Regression Approach," 2005 International Congress, August 23-27, 2005, Copenhagen, Denmark 24737, European Association of Agricultural Economists.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:insuma:v:52:y:2013:i:3:p:477-489. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/locate/inca/505554 .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.