IDEAS home Printed from https://ideas.repec.org/p/arx/papers/1611.02556.html
   My bibliography  Save this paper

Application of the Generalized Linear Models in Actuarial Framework

Author

Listed:
  • Murwan H. M. A. Siddig

Abstract

This paper aims to review the methodology behind the generalized linear models which are used in analyzing the actuarial situations instead of the ordinary multiple linear regression. We introduce how to assess the adequacy of the model which includes comparing nested models using the deviance and the scaled deviance. The Akiake information criterion is proposed as a comprehensive tool for selecting the adequate model. We model a simple automobile portfolio using the generalized linear models, and use the best chosen model to predict the number of claims made by the policyholders in the portfolio.

Suggested Citation

  • Murwan H. M. A. Siddig, 2016. "Application of the Generalized Linear Models in Actuarial Framework," Papers 1611.02556, arXiv.org.
    • Handle: RePEc:arx:papers:1611.02556
    as

    Download full text from publisher

    File URL: http://arxiv.org/pdf/1611.02556
    File Function: Latest version
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Antonio, Katrien & Beirlant, Jan, 2007. "Actuarial statistics with generalized linear mixed models," Insurance: Mathematics and Economics, Elsevier, vol. 40(1), pages 58-76, January.
    2. de Jong,Piet & Heller,Gillian Z., 2008. "Generalized Linear Models for Insurance Data," Cambridge Books, Cambridge University Press, number 9780521879149, June.
    3. Rob Kaas & Marc Goovaerts & Jan Dhaene & Michel Denuit, 2008. "Modern Actuarial Risk Theory," Springer Books, Springer, edition 2, number 978-3-540-70998-5, March.
    4. Andrews, Donald W K, 1991. "Heteroskedasticity and Autocorrelation Consistent Covariance Matrix Estimation," Econometrica, Econometric Society, vol. 59(3), pages 817-858, May.
    5. Verrall, Richard, 1996. "Claims reserving and generalised additive models," Insurance: Mathematics and Economics, Elsevier, vol. 19(1), pages 31-43, December.
    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. Katrien Antonio & Emiliano Valdez, 2012. "Statistical concepts of a priori and a posteriori risk classification in insurance," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 96(2), pages 187-224, June.
    2. Liivika Tee & Meelis Käärik & Rauno Viin, 2017. "On Comparison of Stochastic Reserving Methods with Bootstrapping," Risks, MDPI, vol. 5(1), pages 1-21, January.
    3. Andreas Bayerstadler & Franz Benstetter & Christian Heumann & Fabian Winter, 2014. "A predictive modeling approach to increasing the economic effectiveness of disease management programs," Health Care Management Science, Springer, vol. 17(3), pages 284-301, September.
    4. 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.
    5. 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.
    6. Spark C. Tseung & Ian Weng Chan & Tsz Chai Fung & Andrei L. Badescu & X. Sheldon Lin, 2023. "Improving risk classification and ratemaking using mixture‐of‐experts models with random effects," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 90(3), pages 789-820, September.
    7. Tingting Chen & Anthony Francis Desmond & Peter Adamic, 2023. "Generalized Additive Modelling of Dependent Frequency and Severity Distributions for Aggregate Claims," Journal of Statistical and Econometric Methods, SCIENPRESS Ltd, vol. 12(4), pages 1-1.
    8. Siu, Tak Kuen, 2025. "Threshold Autoregressive Nearest-Neighbour Models for Claims Reserving," Econometrics and Statistics, Elsevier, vol. 33(C), pages 180-208.
    9. Deprez, Laurens & Antonio, Katrien & Boute, Robert, 2021. "Pricing service maintenance contracts using predictive analytics," European Journal of Operational Research, Elsevier, vol. 290(2), pages 530-545.
    10. Baumgartner, Carolin & Gruber, Lutz F. & Czado, Claudia, 2015. "Bayesian total loss estimation using shared random effects," Insurance: Mathematics and Economics, Elsevier, vol. 62(C), pages 194-201.
    11. Xacur, Oscar Alberto Quijano & Garrido, José, 2018. "Bayesian credibility for GLMs," Insurance: Mathematics and Economics, Elsevier, vol. 83(C), pages 180-189.
    12. Katrien Antonio & Jan Beirlant, 2008. "Issues in Claims Reserving and Credibility: A Semiparametric Approach With Mixed Models," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 75(3), pages 643-676, September.
    13. Tzougas, George, 2020. "EM estimation for the Poisson-Inverse Gamma regression model with varying dispersion: an application to insurance ratemaking," LSE Research Online Documents on Economics 106539, London School of Economics and Political Science, LSE Library.
    14. Tzougas, George & Yik, Woo Hee & Mustaqeem, Muhammad Waqar, 2019. "Insurance ratemaking using the Exponential-Lognormal regression model," LSE Research Online Documents on Economics 101729, London School of Economics and Political Science, LSE Library.
    15. Silvie Kafková & Lenka Křivánková, 2014. "Generalized Linear Models in Vehicle Insurance," Acta Universitatis Agriculturae et Silviculturae Mendelianae Brunensis, Mendel University Press, vol. 62(2), pages 383-388.
    16. Matteo Mogliani, 2010. "Residual-based tests for cointegration and multiple deterministic structural breaks: A Monte Carlo study," Working Papers halshs-00564897, HAL.
    17. Marcelo Fernandes & Breno Neri, 2010. "Nonparametric Entropy-Based Tests of Independence Between Stochastic Processes," Econometric Reviews, Taylor & Francis Journals, vol. 29(3), pages 276-306.
    18. Antonia López Villavicencio & Josep Lluís Raymond Bara, 2006. "The short and long-run determinants of the real exchange rate in Mexico," Working Papers wpdea0606, Department of Applied Economics at Universitat Autonoma of Barcelona.
    19. Hansen, Lars Peter & Heaton, John & Luttmer, Erzo G J, 1995. "Econometric Evaluation of Asset Pricing Models," The Review of Financial Studies, Society for Financial Studies, vol. 8(2), pages 237-274.
    20. Cavit Pakel & Neil Shephard & Kevin Sheppard & Robert F. Engle, 2021. "Fitting Vast Dimensional Time-Varying Covariance Models," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 39(3), pages 652-668, July.

    More about this item

    NEP fields

    This paper has been announced in the following NEP Reports:

    Statistics

    Access and download statistics

    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:arx:papers:1611.02556. 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: arXiv administrators (email available below). General contact details of provider: http://arxiv.org/ .

    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.