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EM estimation for the Poisson-Inverse Gamma regression model with varying dispersion: an application to insurance ratemaking

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  • Tzougas, George

Abstract

This article presents the Poisson-Inverse Gamma regression model with varying dispersion for approximating heavy-tailed and overdispersed claim counts. Our main contribution is that we develop an Expectation-Maximization (EM) type algorithm for maximum likelihood (ML) estimation of the Poisson-Inverse Gamma regression model with varying dispersion. The empirical analysis examines a portfolio of motor insurance data in order to investigate the efficiency of the proposed algorithm. Finally, both the a priori and a posteriori, or Bonus-Malus, premium rates that are determined by the Poisson-Inverse Gamma model are compared to those that result from the classic Negative Binomial Type I and the Poisson-Inverse Gaussian distributions with regression structures for their mean and dispersion parameters.

Suggested Citation

  • 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.
    • Handle: RePEc:ehl:lserod:106539
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    References listed on IDEAS

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    Cited by:

    1. Tzougas, George & Jeong, Himchan, 2021. "An expectation-maximization algorithm for the exponential-generalized inverse Gaussian regression model with varying dispersion and shape for modelling the aggregate claim amount," LSE Research Online Documents on Economics 108210, London School of Economics and Political Science, LSE Library.
    2. Tzougas, George & Hong, Natalia & Ho, Ryan, 2022. "Mixed poisson regression models with varying dispersion arising from non-conjugate mixing distributions," LSE Research Online Documents on Economics 113616, London School of Economics and Political Science, LSE Library.
    3. 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.
    4. Tzougas, George & di Cerchiara, Alice Pignatelli, 2021. "Bivariate mixed Poisson regression models with varying dispersion," LSE Research Online Documents on Economics 114327, London School of Economics and Political Science, LSE Library.
    5. Tzougas, George & Pignatelli di Cerchiara, Alice, 2021. "The multivariate mixed Negative Binomial regression model with an application to insurance a posteriori ratemaking," Insurance: Mathematics and Economics, Elsevier, vol. 101(PB), pages 602-625.
    6. Syuhada, Khreshna & Tjahjono, Venansius & Hakim, Arief, 2024. "Compound Poisson–Lindley process with Sarmanov dependence structure and its application for premium-based spectral risk forecasting," Applied Mathematics and Computation, Elsevier, vol. 467(C).

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    More about this item

    Keywords

    poisson-inverse gamma distribution; em algorithm; regression models for mean and dispersion parameters; motor third party liability insurance; ratemaking;
    All these keywords.

    JEL classification:

    • C1 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General

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