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<p>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.</p>

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

  • 期刊论文

  • 发表日期：

    2025年8月4日

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  • Michel Denuit,
  • Julien Trufin,
  • Thomas Verdebout

摘要

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.