IDEAS home Printed from https://ideas.repec.org/a/eee/insuma/v43y2008i2p209-213.html
   My bibliography  Save this article

On the link between credibility and frequency premium

Author

Listed:
  • 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
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0167-6687(08)00078-4
    Download Restriction: Full text for ScienceDirect subscribers only
    ---><---

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

    Other versions of this item:

    References listed on IDEAS

    as
    1. 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.
    2. 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.
    3. Gourieroux, Christian & Monfort, Alain & Trognon, Alain, 1984. "Pseudo Maximum Likelihood Methods: Theory," Econometrica, Econometric Society, vol. 52(3), pages 681-700, May.
    4. Harvey, A C, 1976. "Estimating Regression Models with Multiplicative Heteroscedasticity," Econometrica, Econometric Society, vol. 44(3), pages 461-465, May.
    5. Dufresne, François & Gerber, Hans U. & Shiu, Elias S. W., 1991. "Risk Theory with the Gamma Process," ASTIN Bulletin, Cambridge University Press, vol. 21(2), pages 177-192, 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. 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.
    8. Qian, Weimin, 2000. "An application of nonparametric regression estimation in credibility theory," Insurance: Mathematics and Economics, Elsevier, vol. 27(2), pages 169-176, October.
    9. Hardle, W. & Hall, P. & Ichimura, H., 1991. "Optimal smoothing in single index models," LIDAM Discussion Papers CORE 1991007, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    10. 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.
    11. 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.
    12. Winkelmann, Rainer & Zimmermann, Klaus F., 1991. "A new approach for modeling economic count data," Economics Letters, Elsevier, vol. 37(2), pages 139-143, October.
    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. 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. Bermúdez, Lluís & Karlis, Dimitris, 2012. "A finite mixture of bivariate Poisson regression models with an application to insurance ratemaking," Computational Statistics & Data Analysis, Elsevier, vol. 56(12), pages 3988-3999.
    3. Bermúdez, Lluís & Karlis, Dimitris, 2011. "Bayesian multivariate Poisson models for insurance ratemaking," Insurance: Mathematics and Economics, Elsevier, vol. 48(2), pages 226-236, March.
    4. Bolancé, Catalina & Vernic, Raluca, 2019. "Multivariate count data generalized linear models: Three approaches based on the Sarmanov distribution," Insurance: Mathematics and Economics, Elsevier, vol. 85(C), pages 89-103.
    5. Lluís Bermúdez & Dimitris Karlis & Isabel Morillo, 2020. "Modelling Unobserved Heterogeneity in Claim Counts Using Finite Mixture Models," Risks, MDPI, vol. 8(1), pages 1-13, January.
    6. Ramon Alemany & Catalina Bolancé & Roberto Rodrigo & Raluca Vernic, 2020. "Bivariate Mixed Poisson and Normal Generalised Linear Models with Sarmanov Dependence—An Application to Model Claim Frequency and Optimal Transformed Average Severity," Mathematics, MDPI, vol. 9(1), pages 1-18, December.
    7. 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.
    8. Jean Pinquet, 2012. "Experience rating in non-life insurance," Working Papers hal-00677100, HAL.

    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. Linton, Oliver, 1995. "Second Order Approximation in the Partially Linear Regression Model," Econometrica, Econometric Society, vol. 63(5), pages 1079-1112, September.
    2. Lluís Bermúdez & Dimitris Karlis & Isabel Morillo, 2020. "Modelling Unobserved Heterogeneity in Claim Counts Using Finite Mixture Models," Risks, MDPI, vol. 8(1), pages 1-13, January.
    3. Yang Lu, 2018. "Dynamic Frailty Count Process in Insurance: A Unified Framework for Estimation, Pricing, and Forecasting," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 85(4), pages 1083-1102, December.
    4. 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.
    5. Tzougas, George & Vrontos, Spyridon & Frangos, Nicholas, 2014. "Optimal Bonus-Malus Systems using finite mixture models," LSE Research Online Documents on Economics 70919, London School of Economics and Political Science, LSE Library.
    6. 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.
    7. Gouriéroux, Christian & Monfort, Alain & Tenreiro, Carlos, 1994. "Kernel m-estimators : non parametric diagnostics for structural models," CEPREMAP Working Papers (Couverture Orange) 9405, CEPREMAP.
    8. Qi Li & Jeffrey Scott Racine, 2006. "Nonparametric Econometrics: Theory and Practice," Economics Books, Princeton University Press, edition 1, volume 1, number 8355.
    9. Herwartz, Helmut & Reimers, Hans-Eggert, 2006. "Modelling the Fisher hypothesis: World wide evidence," Economics Working Papers 2006-04, Christian-Albrechts-University of Kiel, Department of Economics.
    10. Severance-Lossin, E. & Sperlich, S., 1995. "Estimation of Derivatives for Additive Separable Models," SFB 373 Discussion Papers 1995,60, Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes.
    11. Hjalmarsson, Erik, 2003. "Does the Black-Scholes formula work for electricity markets? A nonparametric approach," Working Papers in Economics 101, University of Gothenburg, Department of Economics.
    12. Ichimura, Hidehiko & Todd, Petra E., 2007. "Implementing Nonparametric and Semiparametric Estimators," Handbook of Econometrics, in: J.J. Heckman & E.E. Leamer (ed.), Handbook of Econometrics, edition 1, volume 6, chapter 74, Elsevier.
    13. Geng, Xin & Janssens, Wendy & Kramer, Berber, 2018. "Liquid milk: Cash Constraints and Recurring Savings among Dairy Farmers in Kenya," 2018 Annual Meeting, August 5-7, Washington, D.C. 273823, Agricultural and Applied Economics Association.
    14. BERTINELLI, Luisito & STROBL, Eric, 2003. "Urbanization, urban concentration and economic growth in developing countries," LIDAM Discussion Papers CORE 2003076, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    15. Bonsoo Koo & Oliver Linton, 2010. "Semiparametric Estimation of Locally Stationary Diffusion Models," STICERD - Econometrics Paper Series 551, Suntory and Toyota International Centres for Economics and Related Disciplines, LSE.
    16. Zhijie Xiao & Oliver Linton & Raymond J. Carroll & E. Mammen, 2002. "More Efficient Kernel Estimation in Nonparametric Regression with Autocorrelated Errors," Cowles Foundation Discussion Papers 1375, Cowles Foundation for Research in Economics, Yale University.
    17. Dabo-Niang, Sophie & Francq, Christian & Zakoïan, Jean-Michel, 2010. "Combining Nonparametric and Optimal Linear Time Series Predictions," Journal of the American Statistical Association, American Statistical Association, vol. 105(492), pages 1554-1565.
    18. Koop, Gary & Poirier, Dale J., 2004. "Bayesian variants of some classical semiparametric regression techniques," Journal of Econometrics, Elsevier, vol. 123(2), pages 259-282, December.
    19. Labandeira, Xavier & Labeaga, José M. & López-Otero, Xiral, 2017. "A meta-analysis on the price elasticity of energy demand," Energy Policy, Elsevier, vol. 102(C), pages 549-568.
    20. Emmanuel Saez, 2010. "Do Taxpayers Bunch at Kink Points?," American Economic Journal: Economic Policy, American Economic Association, vol. 2(3), pages 180-212, August.

    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:43:y:2008:i:2:p:209-213. 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.