Tweedie dominance for autocalibrated predictors and Laplace transform order

While Krüger and Ziegel [(2021). Generic conditions for forecast dominance. Journal of Business & Economic Statistics, 39(4), 972–983.] defined forecast dominance, or Bregman dominance as dominance for every Bregman loss function, this paper explores Tweedie dominance proposed by Denuit et al. [(2021). Autocalibration and Tweedie dominance for insurance pricing with machine learning. Insurance: Mathematics and Economics, 101, 485–497.] to compare competing candidate premiums. A necessary and sufficient condition is established under autocalibration. Moreover, Laplace transform order turns out to be a sufficient condition for Tweedie dominance between autocalibrated predictors. This shows that Tweedie dominance is a rather weak concept compared to Bregman dominance that reduces to the well-known convex order among autocalibrated predictors.