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Generalized Additive Modelling of Dependent Frequency and Severity Distributions for Aggregate Claims

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  • Tingting Chen
  • Anthony Francis Desmond
  • Peter Adamic

Abstract

This paper examines the problem of accurately estimating the expected value and variance of aggregate claims for each policyholder. Through an appropriate statistical model to estimate the pure premium, an insurer can find niche markets to operate competitively and profitably. To this end, the framework of generalized linear models (GLMs) for aggregate claims is extended to encompass a species of frequentist generalized additive models (GAMs) based on cubic penalized regression splines. The new structure could allow for the incorporation of more flexible nonlinear and/or nonparametric trend terms for the marginal claim frequency, conditional claim severity, and finally for Tweedie modelling as well. This nonparametric approach is illustrated through simulation and applied to an automobile insurance dataset. A juxtaposition of hypothesis test results, AIC values, and attendant graphical diagnostics effectively demonstrate that the GAMs under both the independent and dependent settings give a better fit than the GLM approach. Â JEL classification numbers: C14, G22.

Suggested Citation

  • 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.
    • Handle: RePEc:spt:stecon:v:12:y:2023:i:4:f:12_4_1
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    References listed on IDEAS

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    1. Smyth, Gordon K. & Jørgensen, Bent, 2002. "Fitting Tweedie's Compound Poisson Model to Insurance Claims Data: Dispersion Modelling," ASTIN Bulletin, Cambridge University Press, vol. 32(1), pages 143-157, May.
    2. de Jong,Piet & Heller,Gillian Z., 2008. "Generalized Linear Models for Insurance Data," Cambridge Books, Cambridge University Press, number 9780521879149.
    3. 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.
    4. Jean-Philippe Boucher & Steven Côté & Montserrat Guillen, 2017. "Exposure as Duration and Distance in Telematics Motor Insurance Using Generalized Additive Models," Risks, MDPI, vol. 5(4), pages 1-23, September.
    5. Yi Yang & Wei Qian & Hui Zou, 2018. "Insurance Premium Prediction via Gradient Tree-Boosted Tweedie Compound Poisson Models," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 36(3), pages 456-470, July.
    6. Shi, Peng & Feng, Xiaoping & Ivantsova, Anastasia, 2015. "Dependent frequency–severity modeling of insurance claims," Insurance: Mathematics and Economics, Elsevier, vol. 64(C), pages 417-428.
    7. Stasinopoulos, D. Mikis & Rigby, Robert A., 2007. "Generalized Additive Models for Location Scale and Shape (GAMLSS) in R," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 23(i07).
    8. Ruppert,David & Wand,M. P. & Carroll,R. J., 2003. "Semiparametric Regression," Cambridge Books, Cambridge University Press, number 9780521780506.
    9. Georges Dionne & Christian Gourieroux & Charles Vanasse, 2001. "Testing for Evidence of Adverse Selection in the Automobile Insurance Market: A Comment," Journal of Political Economy, University of Chicago Press, vol. 109(2), pages 444-473, April.
    10. Ruppert,David & Wand,M. P. & Carroll,R. J., 2003. "Semiparametric Regression," Cambridge Books, Cambridge University Press, number 9780521785167.
    11. Garrido, J. & Genest, C. & Schulz, J., 2016. "Generalized linear models for dependent frequency and severity of insurance claims," Insurance: Mathematics and Economics, Elsevier, vol. 70(C), pages 205-215.
    12. Denuit, Michel & Lang, Stefan, 2004. "Non-life rate-making with Bayesian GAMs," Insurance: Mathematics and Economics, Elsevier, vol. 35(3), pages 627-647, December.
    13. Verrall, Richard, 1996. "Claims reserving and generalised additive models," Insurance: Mathematics and Economics, Elsevier, vol. 19(1), pages 31-43, December.
    14. Inyoung Kim & Noah D. Cohen & Raymond J. Carroll, 2003. "Semiparametric Regression Splines in Matched Case-Control Studies," Biometrics, The International Biometric Society, vol. 59(4), pages 1158-1169, December.
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    More about this item

    Keywords

    Premium; Generalized Additive Models; Dependence; Splines; Frequency; Severity.;
    All these keywords.

    JEL classification:

    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
    • G22 - Financial Economics - - Financial Institutions and Services - - - Insurance; Insurance Companies; Actuarial Studies

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