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Recursive partitioning based on gini index for insurance pricing

Author

Listed:
  • Denuit, Michel

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

  • Petit, Robin

    (ULB)

  • Simon, Pierre-Alexandre

    (ULB)

  • Trufin, Julien

    (ULB)

Abstract

Tree-based methods are widely used in insurance studies. By construction, the vector of fitted values increases with respect to majorization order at each split. This ensures that the graph of the Lorenz curve after the split lies below the graph of the Lorenz curve before it. It is therefore meaningful to base to choice of the split on the largest decrease in Lorenz curves, as measured by the area comprised between them. This turns out to be equivalent to partition data according to the largest increase in Gini index. Also, this proposal is intimately relatedto convex order which coincides with Bregman order under auto-calibration. Besides theseattractive theoretical properties, the proposed splitting rule poses computational challengesthat are solved by an appropriate C++ implementation. The effectiveness of the proposedapproach is illustrated with a case study performed on a Belgian motor third-party liability insurance portfolio.

Suggested Citation

  • Denuit, Michel & Petit, Robin & Simon, Pierre-Alexandre & Trufin, Julien, 2025. "Recursive partitioning based on gini index for insurance pricing," LIDAM Discussion Papers ISBA 2025025, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    • Handle: RePEc:aiz:louvad:2025025
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