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Experience rating with Poisson mixtures

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  • Brown, Garfield O.
  • Buckley, Winston S.

Abstract

We propose a Poisson mixture model for count data to determine the number of groups in a Group Life insurance portfolio consisting of claim numbers or deaths. We take a non-parametric Bayesian approach to modelling this mixture distribution using a Dirichlet process prior and use reversible jump Markov chain Monte Carlo to estimate the number of components in the mixture. Unlike Haastrup, we show that the assumption of identical heterogeneity for all groups may not hold as 88% of the posterior probability is assigned to models with two or three components, and 11% to models with four or five components, whereas models with one component are never visited. Our major contribution is showing how to account for both model uncertainty and parameter estimation within a single framework.

Suggested Citation

  • Brown, Garfield O. & Buckley, Winston S., 2015. "Experience rating with Poisson mixtures," Annals of Actuarial Science, Cambridge University Press, vol. 9(2), pages 304-321, September.
    • Handle: RePEc:cup:anacsi:v:9:y:2015:i:02:p:304-321_00
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    Citations

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    Cited by:

    1. Iain L. MacDonald, 2021. "Is EM really necessary here? Examples where it seems simpler not to use EM," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 105(4), pages 629-647, December.
    2. Tatjana Miljkovic & Daniel Fernández, 2018. "On Two Mixture-Based Clustering Approaches Used in Modeling an Insurance Portfolio," Risks, MDPI, vol. 6(2), pages 1-18, May.
    3. Mengyu Yu & Mazie Krehbiel & Samantha Thompson & Tatjana Miljkovic, 2020. "An exploration of gender gap using advanced data science tools: actuarial research community," Scientometrics, Springer;Akadémiai Kiadó, vol. 123(2), pages 767-789, May.
    4. Antonio Canale & Igor Prünster, 2017. "Robustifying Bayesian nonparametric mixtures for count data," Biometrics, The International Biometric Society, vol. 73(1), pages 174-184, March.
    5. Jennifer S. K. Chan & S. T. Boris Choy & Udi Makov & Ariel Shamir & Vered Shapovalov, 2022. "Variable Selection Algorithm for a Mixture of Poisson Regression for Handling Overdispersion in Claims Frequency Modeling Using Telematics Car Driving Data," Risks, MDPI, vol. 10(4), pages 1-10, April.
    6. Verschuren, Robert Matthijs, 2022. "Frequency-severity experience rating based on latent Markovian risk profiles," Insurance: Mathematics and Economics, Elsevier, vol. 107(C), pages 379-392.
    7. 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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