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A class of mixture of experts models for general insurance: Theoretical developments

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  • Fung, Tsz Chai
  • Badescu, Andrei L.
  • Lin, X. Sheldon

Abstract

In the Property and Casualty (P&C) ratemaking process, it is critical to understand the effect of policyholders’ risk profile to the number and amount of claims, the dependence among various business lines and the claim distributions. To include all the above features, it is essential to develop a regression model which is flexible and theoretically justified. Motivated by the issues above, we propose a class of logit-weighted reduced mixture of experts (LRMoE) models for multivariate claim frequencies or severities distributions. LRMoE is interpretable, as it has two components: Gating functions, which classify policyholders into various latent sub-classes; and Expert functions, which govern the distributional properties of the claims. Also, upon the development of denseness theory in regression setting, we can heuristically interpret the LRMoE as a “fully flexible” model to capture any distributional, dependence and regression structures subject to a denseness condition. Further, the mathematical tractability of the LRMoE is guaranteed since it satisfies various marginalization and moment properties. Finally, we discuss some special choices of expert functions that make the corresponding LRMoE “fully flexible”. In the subsequent paper (Fung et al., 2019b), we will focus on the estimation and application aspects of the LRMoE.

Suggested Citation

  • Fung, Tsz Chai & Badescu, Andrei L. & Lin, X. Sheldon, 2019. "A class of mixture of experts models for general insurance: Theoretical developments," Insurance: Mathematics and Economics, Elsevier, vol. 89(C), pages 111-127.
  • Handle: RePEc:eee:insuma:v:89:y:2019:i:c:p:111-127
    DOI: 10.1016/j.insmatheco.2019.09.007
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    Cited by:

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    2. Chen, Zezhun Chen & Dassios, Angelos & Tzougas, George, 2024. "EM estimation for bivariate mixed poisson INAR(1) claim count regression models with correlated random effects," LSE Research Online Documents on Economics 118826, London School of Economics and Political Science, LSE Library.
    3. George Tzougas & Despoina Makariou, 2022. "The multivariate Poisson‐Generalized Inverse Gaussian claim count regression model with varying dispersion and shape parameters," Risk Management and Insurance Review, American Risk and Insurance Association, vol. 25(4), pages 401-417, December.
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    5. 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.
    6. 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.
    7. Tzougas, George & Makariou, Despoina, 2022. "The multivariate Poisson-Generalized Inverse Gaussian claim count regression model with varying dispersion and shape parameters," LSE Research Online Documents on Economics 117197, London School of Economics and Political Science, LSE Library.
    8. Počuča, Nikola & Jevtić, Petar & McNicholas, Paul D. & Miljkovic, Tatjana, 2020. "Modeling frequency and severity of claims with the zero-inflated generalized cluster-weighted models," Insurance: Mathematics and Economics, Elsevier, vol. 94(C), pages 79-93.
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    10. Despoina Makariou & Pauline Barrieu & George Tzougas, 2021. "A Finite Mixture Modelling Perspective for Combining Experts’ Opinions with an Application to Quantile-Based Risk Measures," Risks, MDPI, vol. 9(6), pages 1-25, June.

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