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Concordance Probability for Insurance Pricing Models

Author

Listed:
  • Jolien Ponnet

    (Department of Mathematics, Katholieke Universiteit Leuven, 3000 Leuven, Belgium)

  • Robin Van Oirbeek

    (Data Office, Allianz Benelux, 1000 Brussels, Belgium
    Department of Mathematics, University of Antwerp, 2020 Antwerp, Belgium)

  • Tim Verdonck

    (Department of Mathematics, Katholieke Universiteit Leuven, 3000 Leuven, Belgium
    Department of Mathematics, University of Antwerp, 2020 Antwerp, Belgium)

Abstract

The concordance probability, also called the C-index, is a popular measure to capture the discriminatory ability of a predictive model. In this article, the definition of this measure is adapted to the specific needs of the frequency and severity model, typically used during the technical pricing of a non-life insurance product. For the frequency model, the need of two different groups is tackled by defining three new types of the concordance probability. Secondly, these adapted definitions deal with the concept of exposure, which is the duration of a policy or insurance contract. Frequency data typically have a large sample size and therefore we present two fast and accurate estimation procedures for big data. Their good performance is illustrated on two real-life datasets. Upon these examples, we also estimate the concordance probability developed for severity models.

Suggested Citation

  • Jolien Ponnet & Robin Van Oirbeek & Tim Verdonck, 2021. "Concordance Probability for Insurance Pricing Models," Risks, MDPI, vol. 9(10), pages 1-26, October.
    • Handle: RePEc:gam:jrisks:v:9:y:2021:i:10:p:178-:d:651452
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    References listed on IDEAS

    as
    1. 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.
    2. Legrand, Catherine, 2021. "Advanced Survival Models," LIDAM Reprints ISBA 2021015, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    3. 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).
    4. 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).
    5. Jean-Philippe Boucher & Michel Denuit & Montserrat Guillén, 2007. "Risk Classification for Claim Counts," North American Actuarial Journal, Taylor & Francis Journals, vol. 11(4), pages 110-131.
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