IDEAS home Printed from https://ideas.repec.org/a/eee/insuma/v70y2016icp339-353.html
   My bibliography  Save this article

On the credibility of insurance claim frequency: Generalized count models and parametric estimators

Author

Listed:
  • Asamoah, Kwadwo

Abstract

We analyze the concept of credibility in claim frequency in two generalized count models–Mittag-Leffler and Weibull count models–which can handle both underdispersion and overdispersion in count data and nest the commonly used Poisson model as a special case. We find evidence, using data from a Danish insurance company, that the simple Poisson model can set the credibility weight to one even when there are only three years of individual experience data resulting from large heterogeneity among policyholders, and in doing so, it can thus break down the credibility model. The generalized count models, on the other hand, allow the weight to adjust according to the number of years of experience available. We propose parametric estimators for the structural parameters in the credibility formula using the mean and variance of the assumed distributions and a maximum likelihood estimation over a collective data. As an example, we show that the proposed parameters from Mittag-Leffler provide weights that are consistent with the idea of credibility. A simulation study is carried out investigating the stability of the maximum likelihood estimates from the Weibull count model. Finally, we extend the analyses to multidimensional lines and explain how our approach can be used in selecting profitable customers in cross-selling; customers can now be selected by estimating a function of their unknown risk profiles, which is the mean of the assumed distribution on their number of claims.

Suggested Citation

  • Asamoah, Kwadwo, 2016. "On the credibility of insurance claim frequency: Generalized count models and parametric estimators," Insurance: Mathematics and Economics, Elsevier, vol. 70(C), pages 339-353.
  • Handle: RePEc:eee:insuma:v:70:y:2016:i:c:p:339-353
    DOI: 10.1016/j.insmatheco.2016.07.003
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0167668716301342
    Download Restriction: Full text for ScienceDirect subscribers only

    File URL: https://libkey.io/10.1016/j.insmatheco.2016.07.003?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. Bichsel, Fritz, 1967. "Experience Rating in Subsets of Risks," ASTIN Bulletin, Cambridge University Press, vol. 4(3), pages 210-227, July.
    2. Englund, Martin & Guillén, Montserrat & Gustafsson, Jim & Nielsen, Lars Hougaard & Nielsen, Jens Perch, 2008. "Multivariate Latent Risk: A Credibility Approach," ASTIN Bulletin, Cambridge University Press, vol. 38(1), pages 137-146, May.
    3. Pinquet, Jean, 1998. "Designing Optimal Bonus-Malus Systems from Different Types of Claims," ASTIN Bulletin, Cambridge University Press, vol. 28(2), pages 205-220, November.
    4. Kanichukattu K. Jose & Bindu Abraham, 2011. "A count model based on Mittag-Leffler interarrival times," Statistica, Department of Statistics, University of Bologna, vol. 71(4), pages 501-514.
    5. Pinquet, Jean, 1997. "Allowance for Cost of Claims in Bonus-Malus Systems," ASTIN Bulletin, Cambridge University Press, vol. 27(1), pages 33-57, May.
    6. Desjardins, Denise & Dionne, Georges & Pinquet, Jean, 2001. "Experience Rating Schemes for Fleets of Vehicles," ASTIN Bulletin, Cambridge University Press, vol. 31(1), pages 81-105, May.
    7. repec:bot:journl:v:71:y:2011:i:4:p:501-514 is not listed on IDEAS
    8. B. Larivière & D. Van Den Poel, 2004. "Investigating the role of product features in preventing customer churn, by using survival analysis and choice modeling: The case of financial services," Working Papers of Faculty of Economics and Business Administration, Ghent University, Belgium 04/223, Ghent University, Faculty of Economics and Business Administration.
    9. Zehnwirth, Ben, 1985. "Linear Filtering and Recursive Credibility Estimation," ASTIN Bulletin, Cambridge University Press, vol. 15(1), pages 19-35, April.
    10. M. Tolga Akçura & Kannan Srinivasan, 2005. "Research Note: Customer Intimacy and Cross-Selling Strategy," Management Science, INFORMS, vol. 51(6), pages 1007-1012, June.
    11. McShane, Blake & Adrian, Moshe & Bradlow, Eric T & Fader, Peter S, 2008. "Count Models Based on Weibull Interarrival Times," Journal of Business & Economic Statistics, American Statistical Association, vol. 26, pages 369-378.
    12. Norberg, Ragnar, 1982. "On optimal parameter estimation in credibility," Insurance: Mathematics and Economics, Elsevier, vol. 1(2), pages 73-89, April.
    13. Martin Englund & Jim Gustafsson & Jens Perch Nielsen & Fredrik Thuring, 2009. "Multidimensional Credibility With Time Effects: An Application to Commercial Business Lines," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 76(2), pages 443-453, June.
    14. Cameron, A Colin & Johansson, Per, 1997. "Count Data Regression Using Series Expansions: With Applications," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 12(3), pages 203-223, May-June.
    Full references (including those not matched with items on IDEAS)

    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. Levon Barseghyan & Francesca Molinari & Darcy Steeg Morris & Joshua C. Teitelbaum, 2020. "The Cost of Legal Restrictions on Experience Rating," Journal of Empirical Legal Studies, John Wiley & Sons, vol. 17(1), pages 38-70, March.
    2. Angers, Jean-François & Desjardins, Denise & Dionne, Georges & Guertin, François, 2006. "Vehicle and Fleet Random Effects in a Model of Insurance Rating for Fleets of Vehicles," ASTIN Bulletin, Cambridge University Press, vol. 36(1), pages 25-77, May.
    3. Angers, Jean-François & Desjardins, Denise & Dionne, Georges, 2004. "Modèle Bayésien de tarification de l’assurance des flottes de véhicules," L'Actualité Economique, Société Canadienne de Science Economique, vol. 80(2), pages 253-303, Juin-Sept.
    4. 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.
    5. Jean Pinquet, 2012. "Experience rating in non-life insurance," Working Papers hal-00677100, HAL.
    6. Pechon, Florian & Denuit, Michel & Trufin, Julien, 2018. "Multivariate Modelling of Multiple Guarantees in Motor Insurance of a Household," LIDAM Discussion Papers ISBA 2018019, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    7. Payandeh Najafabadi Amir T. & MohammadPour Saeed, 2018. "A k-Inflated Negative Binomial Mixture Regression Model: Application to Rate–Making Systems," Asia-Pacific Journal of Risk and Insurance, De Gruyter, vol. 12(2), pages 1-31, July.
    8. 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.
    9. Joanna Sawicka, 2013. "Model stochastycznej zależności liczby szkód i wartości pojedynczej szkody," Collegium of Economic Analysis Annals, Warsaw School of Economics, Collegium of Economic Analysis, issue 31, pages 157-183.
    10. Frees, Edward W. & Wang, Ping, 2006. "Copula credibility for aggregate loss models," Insurance: Mathematics and Economics, Elsevier, vol. 38(2), pages 360-373, April.
    11. Michel Denuit & Yang Lu, 2021. "Wishart‐gamma random effects models with applications to nonlife insurance," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 88(2), pages 443-481, June.
    12. Olena Ragulina, 2017. "Bonus--malus systems with different claim types and varying deductibles," Papers 1707.00917, arXiv.org.
    13. 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.
    14. Martin Englund & Jim Gustafsson & Jens Perch Nielsen & Fredrik Thuring, 2009. "Multidimensional Credibility With Time Effects: An Application to Commercial Business Lines," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 76(2), pages 443-453, June.
    15. Daniel Sobiecki, 2015. "Experience rating with dependence between MTPL and MOD claims," Collegium of Economic Analysis Annals, Warsaw School of Economics, Collegium of Economic Analysis, issue 37, pages 269-282.
    16. Desjardins, Denise & Dionne, Georges & Pinquet, Jean, 2001. "Experience Rating Schemes for Fleets of Vehicles," ASTIN Bulletin, Cambridge University Press, vol. 31(1), pages 81-105, May.
    17. Tzougas, George & Hoon, W. L. & Lim, J. M., 2019. "The negative binomial-inverse Gaussian regression model with an application to insurance ratemaking," LSE Research Online Documents on Economics 101728, London School of Economics and Political Science, LSE Library.
    18. Lee, Woojoo & Kim, Jeonghwan & Ahn, Jae Youn, 2020. "The Poisson random effect model for experience ratemaking: Limitations and alternative solutions," Insurance: Mathematics and Economics, Elsevier, vol. 91(C), pages 26-36.
    19. Tzougas, George & Vrontos, Spyridon & Frangos, Nicholas, 2018. "Bonus-Malus systems with two component mixture models arising from different parametric families," LSE Research Online Documents on Economics 84301, London School of Economics and Political Science, LSE Library.
    20. George Tzougas, 2020. "EM Estimation for the Poisson-Inverse Gamma Regression Model with Varying Dispersion: An Application to Insurance Ratemaking," Risks, MDPI, vol. 8(3), pages 1-23, September.

    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:70:y:2016:i:c:p:339-353. 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.