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Insurance Premium Prediction via Gradient Tree-Boosted Tweedie Compound Poisson Models

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  • Yi Yang
  • Wei Qian
  • Hui Zou

Abstract

The Tweedie GLM is a widely used method for predicting insurance premiums. However, the structure of the logarithmic mean is restricted to a linear form in the Tweedie GLM, which can be too rigid for many applications. As a better alternative, we propose a gradient tree-boosting algorithm and apply it to Tweedie compound Poisson models for pure premiums. We use a profile likelihood approach to estimate the index and dispersion parameters. Our method is capable of fitting a flexible nonlinear Tweedie model and capturing complex interactions among predictors. A simulation study confirms the excellent prediction performance of our method. As an application, we apply our method to an auto-insurance claim data and show that the new method is superior to the existing methods in the sense that it generates more accurate premium predictions, thus helping solve the adverse selection issue. We have implemented our method in a user-friendly R package that also includes a nice visualization tool for interpreting the fitted model.

Suggested Citation

  • Yi Yang & Wei Qian & Hui Zou, 2018. "Insurance Premium Prediction via Gradient Tree-Boosted Tweedie Compound Poisson Models," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 36(3), pages 456-470, July.
  • Handle: RePEc:taf:jnlbes:v:36:y:2018:i:3:p:456-470
    DOI: 10.1080/07350015.2016.1200981
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    Citations

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    Cited by:

    1. Qian, Wei & Rolling, Craig A. & Cheng, Gang & Yang, Yuhong, 2022. "Combining forecasts for universally optimal performance," International Journal of Forecasting, Elsevier, vol. 38(1), pages 193-208.
    2. Freek Holvoet & Katrien Antonio & Roel Henckaerts, 2023. "Neural networks for insurance pricing with frequency and severity data: a benchmark study from data preprocessing to technical tariff," Papers 2310.12671, arXiv.org, revised Oct 2023.
    3. Christopher Blier-Wong & Hélène Cossette & Luc Lamontagne & Etienne Marceau, 2020. "Machine Learning in P&C Insurance: A Review for Pricing and Reserving," Risks, MDPI, vol. 9(1), pages 1-26, December.
    4. Trufin, Julien & Denuit, Michel, 2021. "Boosting cost-complexity pruned trees On Tweedie responses: the ABT machine," LIDAM Discussion Papers ISBA 2021015, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    5. Dong-Young Lim, 2021. "A Neural Frequency-Severity Model and Its Application to Insurance Claims," Papers 2106.10770, arXiv.org, revised Feb 2024.
    6. Zhiyu Quan & Changyue Hu & Panyi Dong & Emiliano A. Valdez, 2024. "Improving Business Insurance Loss Models by Leveraging InsurTech Innovation," Papers 2401.16723, arXiv.org.
    7. Kevin Kuo & Daniel Lupton, 2020. "Towards Explainability of Machine Learning Models in Insurance Pricing," Papers 2003.10674, arXiv.org.
    8. Viktor Stojkoski & Petar Jolakoski & Igor Ivanovski, 2021. "The short‐run impact of COVID‐19 on the activity in the insurance industry in the Republic of North Macedonia," Risk Management and Insurance Review, American Risk and Insurance Association, vol. 24(3), pages 221-242, September.
    9. Tingting Chen & Anthony Francis Desmond & Peter Adamic, 2023. "Generalized Additive Modelling of Dependent Frequency and Severity Distributions for Aggregate Claims," Journal of Statistical and Econometric Methods, SCIENPRESS Ltd, vol. 12(4), pages 1-1.
    10. Hainaut, Donatien & Trufin, Julien & Denuit, Michel, 2021. "Response versus gradient boosting trees, GLMs and neural networks under Tweedie loss and log-link," LIDAM Discussion Papers ISBA 2021012, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    11. Hu, Changyue & Quan, Zhiyu & Chong, Wing Fung, 2022. "Imbalanced learning for insurance using modified loss functions in tree-based models," Insurance: Mathematics and Economics, Elsevier, vol. 106(C), pages 13-32.
    12. Carina Clemente & Gracinda R. Guerreiro & Jorge M. Bravo, 2023. "Modelling Motor Insurance Claim Frequency and Severity Using Gradient Boosting," Risks, MDPI, vol. 11(9), pages 1-20, September.
    13. Simon CK Lee, 2020. "Delta Boosting Implementation of Negative Binomial Regression in Actuarial Pricing," Risks, MDPI, vol. 8(1), pages 1-21, February.
    14. Xiaoshan Su & Manying Bai, 2020. "Stochastic gradient boosting frequency-severity model of insurance claims," PLOS ONE, Public Library of Science, vol. 15(8), pages 1-24, August.
    15. Wei Qian & Craig A. Rolling & Gang Cheng & Yuhong Yang, 2019. "On the Forecast Combination Puzzle," Econometrics, MDPI, vol. 7(3), pages 1-26, September.

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