Comparison of predictors’ performance in insurance pricing: testing for Bregman dominance based on Murphy diagrams

Michel Denuit, Julien Trufin and Thomas Verdebout
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Michel Denuit: Université catholique de Louvain, LIDAM/ISBA, Belgium
Julien Trufin: Université Libre de Bruxelles
Thomas Verdebout: Université Libre de Bruxelles

No 2025015, LIDAM Reprints ISBA from Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA)

Abstract: Ehm et al. (2016) defined forecast dominance, or Bregman dominance as dominance for every Bregman loss function. This letter explores Bregman dominance to compare competing candidate pure premiums. An actuarial interpretation is given for the expectation of extremal consistent loss functions characterizing Bregman dominance, showing their relevance in the context of insurance pricing. An effective testing procedure for Bregman dominance is proposed based on Murphy diagrams and its performance is evaluated through a simulation study. Compared to the existing literature, the proposed testing procedure is easier because it exploits the independence and homogeneity assumptions made in insurance studies and focuses on the conditional mean. An application to a Swiss motor insurance data set demonstrates the potential of the proposed procedure.

Keywords: Insurance pricing; Model comparison; Bregman dominance; Murphy diagram; Statistical test (search for similar items in EconPapers)
Pages: 12
Date: 2025-08-04
Note: In: European Actuarial Journal, 2025, vol. 15, p. 493-504
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Persistent link: https://EconPapers.repec.org/RePEc:aiz:louvar:2025015

DOI: 10.1007/s13385-025-00429-4

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