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Frequency-severity experience rating based on latent Markovian risk profiles

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  • Verschuren, Robert Matthijs

Abstract

Bonus-Malus Systems traditionally consider a customer's number of claims irrespective of their sizes, even though these components are dependent in practice. We propose a novel joint experience rating approach based on latent Markovian risk profiles to allow for a positive or negative individual frequency-severity dependence. The latent profiles evolve over time in a Hidden Markov Model to capture updates in a customer's claims experience, making claim counts and sizes conditionally independent. We show that the resulting risk premia lead to a dynamic, claims experience-weighted mixture of standard credibility premia. The proposed approach is applied to a Dutch automobile insurance portfolio and identifies customer risk profiles with distinctive claiming behavior. These profiles, in turn, enable us to better distinguish between customer risks.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:insuma:v:107:y:2022:i:c:p:379-392
    DOI: 10.1016/j.insmatheco.2022.09.007
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    Cited by:

    1. Simon, Pierre-Alexandre & Trufin, Julien & Denuit, Michel, 2023. "Bivariate Poisson credibility model and bonus-malus scale for claim and near-claim events," LIDAM Discussion Papers ISBA 2023014, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).

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    More about this item

    Keywords

    Experience rating; Frequency-severity dependence; Dynamic latent risk profiles; Hidden Markov model; Automobile insurance;
    All these keywords.

    JEL classification:

    • C32 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes; State Space Models
    • C33 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Models with Panel Data; Spatio-temporal Models
    • C53 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Forecasting and Prediction Models; Simulation Methods
    • G22 - Financial Economics - - Financial Institutions and Services - - - Insurance; Insurance Companies; Actuarial Studies

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