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Autocalibration by balance correction in nonlife insurance pricing

Author

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  • Denuit, Michel

    (Université catholique de Louvain, LIDAM/ISBA, Belgium)

  • Trufin, Julien

    (ULB)

Abstract

By exploiting massive amounts of data, machine learning techniques provide actuaries with predictors exhibiting high correlation with claim frequencies and severities. However, these predictors generally fail to achieve financial equilibrium and thus do not qualify as pure premiums. Autocalibration effectively addresses this issue since it ensures that every group of policyholders paying the same premium is on average self-financing, as demonstrated by Denuit et al. (2021), Ciatto et al. (2022), Lindholm et al. (2022) and Wüthrich (2022). These authors proposed balance correction as a way to make any candidate premium autocalibrated. The present paper further studies the effect of balance correction on resulting pure premiums. It is shown that this method is also beneficial in terms of out-of-sample, or predictive Tweedie deviance, Bregman divergence as well as concentration curves. The paper then derives conditions ensuring that the initial predictor and its balance-corrected version are ordered in Lorenz order. Finally, criteria are proposed to rank the balance-corrected versions of two competing predictors in the convex order.

Suggested Citation

  • Denuit, Michel & Trufin, Julien, 2022. "Autocalibration by balance correction in nonlife insurance pricing," LIDAM Discussion Papers ISBA 2022041, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    • Handle: RePEc:aiz:louvad:2022041
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    References listed on IDEAS

    as
    1. Michel Denuit & Arthur Charpentier & Julien Trufin, 2021. "Autocalibration and Tweedie-dominance for Insurance Pricing with Machine Learning," Papers 2103.03635, arXiv.org, revised Jul 2021.
    2. Gneiting, Tilmann, 2011. "Making and Evaluating Point Forecasts," Journal of the American Statistical Association, American Statistical Association, vol. 106(494), pages 746-762.
    3. Denuit, Michel & Trufin, Julien, 2021. "Lorenz curve, Gini coefficient, and Tweedie dominance for autocalibrated predictors," LIDAM Discussion Papers ISBA 2021036, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    4. Patton, Andrew J., 2011. "Volatility forecast comparison using imperfect volatility proxies," Journal of Econometrics, Elsevier, vol. 160(1), pages 246-256, January.
    5. Denuit, Michel & Charpentier, Arthur & Trufin, Julien, 2021. "Autocalibration and Tweedie-dominance for insurance pricing with machine learning," LIDAM Discussion Papers ISBA 2021013, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    6. Denuit, Michel & Trufin, Julien, 2022. "Model selection with Pearson’s correlation, concentration and Lorenz curves under autocalibration," LIDAM Discussion Papers ISBA 2022033, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    7. Denuit, Michel & Charpentier , Arthur & Trufin, Julien, 2021. "Autocalibration and Tweedie-dominance for insurance pricing with machine learning," LIDAM Reprints ISBA 2021049, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    8. Andrew J. Patton, 2020. "Comparing Possibly Misspecified Forecasts," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 38(4), pages 796-809, October.
    9. Denuit, Michel, 2010. "Positive dependence of signals," LIDAM Discussion Papers ISBA 2010025, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    10. Denuit, Michel & Sznajder, Dominik & Trufin, Julien, 2019. "Model selection based on Lorenz and concentration curves, Gini indices and convex order," LIDAM Reprints ISBA 2019046, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    11. Denuit, Michel & Charpentier, Arthur & Trufin, Julien, 2021. "Autocalibration and Tweedie-dominance for insurance pricing with machine learning," Insurance: Mathematics and Economics, Elsevier, vol. 101(PB), pages 485-497.
    12. Denuit, Michel & Sznajder, Dominik & Trufin, Julien, 2019. "Model selection based on Lorenz and concentration curves, Gini indices and convex order," Insurance: Mathematics and Economics, Elsevier, vol. 89(C), pages 128-139.
    13. Denuit, Michel & Sznajder, Dominik & Trufin, Julien, 2019. "Model selection based on Lorenz and concentration curves, Gini indices and convex order," LIDAM Discussion Papers ISBA 2019006, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    14. Fabian Krüger & Johanna F. Ziegel, 2021. "Generic Conditions for Forecast Dominance," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 39(4), pages 972-983, October.
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    Keywords

    Tweedie deviance ; Bregman divergence ; financial equilibrium ; convex order ; Lorenz order;
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