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An Expectation-Maximization Algorithm for the Exponential-Generalized Inverse Gaussian Regression Model with Varying Dispersion and Shape for Modelling the Aggregate Claim Amount

Author

Listed:
  • George Tzougas

    (Department of Statistics, London School of Economics and Political Science, London WC2A 2AE, UK)

  • Himchan Jeong

    (Department of Statistics and Actuarial Science, Simon Fraser University, 8888 University Drive, Burnaby, BC V5A 1S6, Canada)

Abstract

This article presents the Exponential–Generalized Inverse Gaussian regression model with varying dispersion and shape. The EGIG is a general distribution family which, under the adopted modelling framework, can provide the appropriate level of flexibility to fit moderate costs with high frequencies and heavy-tailed claim sizes, as they both represent significant proportions of the total loss in non-life insurance. The model’s implementation is illustrated by a real data application which involves fitting claim size data from a European motor insurer. The maximum likelihood estimation of the model parameters is achieved through a novel Expectation Maximization (EM)-type algorithm that is computationally tractable and is demonstrated to perform satisfactorily.

Suggested Citation

  • George Tzougas & Himchan Jeong, 2021. "An Expectation-Maximization Algorithm for the Exponential-Generalized Inverse Gaussian Regression Model with Varying Dispersion and Shape for Modelling the Aggregate Claim Amount," Risks, MDPI, vol. 9(1), pages 1-17, January.
    • Handle: RePEc:gam:jrisks:v:9:y:2021:i:1:p:19-:d:477237
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    References listed on IDEAS

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    1. Tzougas, George & Karlis, Dimitris, 2020. "An Em Algorithm For Fitting A New Class Of Mixed Exponential Regression Models With Varying Dispersion," ASTIN Bulletin, Cambridge University Press, vol. 50(2), pages 555-583, May.
    2. 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.
    3. Jeong, Himchan, 2020. "Testing For Random Effects In Compound Risk Models Via Bregman Divergence," ASTIN Bulletin, Cambridge University Press, vol. 50(3), pages 777-798, September.
    4. Rigby, R.A. & Stasinopoulos, D.M. & Akantziliotou, C., 2008. "A framework for modelling overdispersed count data, including the Poisson-shifted generalized inverse Gaussian distribution," Computational Statistics & Data Analysis, Elsevier, vol. 53(2), pages 381-393, December.
    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. Frees, Edward W. & Valdez, Emiliano A., 2008. "Hierarchical Insurance Claims Modeling," Journal of the American Statistical Association, American Statistical Association, vol. 103(484), pages 1457-1469.
    7. Laudagé, Christian & Desmettre, Sascha & Wenzel, Jörg, 2019. "Severity modeling of extreme insurance claims for tariffication," Insurance: Mathematics and Economics, Elsevier, vol. 88(C), pages 77-92.
    8. Marjorie Rosenberg & Edward Frees & Jiafeng Sun & Paul Johnson & Jim Robinson, 2007. "Predictive Modeling with Longitudinal Data," North American Actuarial Journal, Taylor & Francis Journals, vol. 11(3), pages 54-69.
    9. Yang, Xipei & Frees, Edward W. & Zhang, Zhengjun, 2011. "A generalized beta copula with applications in modeling multivariate long-tailed data," Insurance: Mathematics and Economics, Elsevier, vol. 49(2), pages 265-284, September.
    10. Tzougas, George & Yik, Woo Hee & Mustaqeem, Muhammad Waqar, 2020. "Insurance ratemaking using the Exponential-Lognormal regression model," Annals of Actuarial Science, Cambridge University Press, vol. 14(1), pages 42-71, March.
    11. Wang, Yinzhi & Hobæk Haff, Ingrid & Huseby, Arne, 2020. "Modelling extreme claims via composite models and threshold selection methods," Insurance: Mathematics and Economics, Elsevier, vol. 91(C), pages 257-268.
    12. Frangos, Nikolaos & Karlis, Dimitris, 2004. "Modelling losses using an exponential-inverse Gaussian distribution," Insurance: Mathematics and Economics, Elsevier, vol. 35(1), pages 53-67, August.
    13. Enrique Calderín-Ojeda & Kevin Fergusson & Xueyuan Wu, 2017. "An EM Algorithm for Double-Pareto-Lognormal Generalized Linear Model Applied to Heavy-Tailed Insurance Claims," Risks, MDPI, vol. 5(4), pages 1-24, November.
    14. Ahn, Soohan & Kim, Joseph H.T. & Ramaswami, Vaidyanathan, 2012. "A new class of models for heavy tailed distributions in finance and insurance risk," Insurance: Mathematics and Economics, Elsevier, vol. 51(1), pages 43-52.
    15. Bhati, Deepesh & Ravi, Sreenivasan, 2018. "On generalized log-Moyal distribution: A new heavy tailed size distribution," Insurance: Mathematics and Economics, Elsevier, vol. 79(C), pages 247-259.
    16. Tzougas, George & Karlis, Dimitris, 2020. "An EM algorithm for fitting a new class of mixed exponential regression models with varying dispersion," LSE Research Online Documents on Economics 104027, London School of Economics and Political Science, LSE Library.
    17. Beirlant, J. & Derveaux, V. & De Meyer, A. M. & Goovaerts, M. J. & Labie, E. & Maenhoudt, B., 1992. "Statistical risk evaluation applied to (Belgian) car insurance," Insurance: Mathematics and Economics, Elsevier, vol. 10(4), pages 289-302, January.
    18. Edward W. Frees & Gee Lee & Lu Yang, 2016. "Multivariate Frequency-Severity Regression Models in Insurance," Risks, MDPI, vol. 4(1), pages 1-36, February.
    19. Jeong, Himchan & Valdez, Emiliano A., 2020. "Predictive compound risk models with dependence," Insurance: Mathematics and Economics, Elsevier, vol. 94(C), pages 182-195.
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    Cited by:

    1. Gao, Guangyuan & Meng, Shengwang & Shi, Yanlin, 2021. "Dispersion modelling of outstanding claims with double Poisson regression models," Insurance: Mathematics and Economics, Elsevier, vol. 101(PB), pages 572-586.

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