par Denuit, Michel 
;Petit, Robin ;Simon, Pierre-Alexandre ;Trufin, Julien
Référence European Actuarial Journal
Publication A Paraître, 2026-02-01
;Petit, Robin ;Simon, Pierre-Alexandre ;Trufin, Julien Référence European Actuarial Journal
Publication A Paraître, 2026-02-01
Article révisé par les pairs
| Résumé : | 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 related to convex order which coincides with Bregman order under auto-calibration. Besides these attractive theoretical properties, the proposed splitting rule poses computational challenges that are solved by an appropriate C++ implementation. The effectiveness of the proposed approach is illustrated with a case study performed on a Belgian motor third-party liability insurance portfolio. |
