Two Moments for Risk-Monotone Additive Statistics

Mark Whitmeyer

Two Moments for Risk-Monotone Additive Statistics

Theoretical Economics 2026-08-11 v1 Probability

Authors: Mark Whitmeyer

Abstract

Every statistic on laws with finite pth moment that is additive across independent risks and monotone in mean-preserving spreads depends only on an additive function of the mean when p is strictly less than 2, and only on such a function and a nonnegative multiple of the variance when p is no less than 2.

Keywords

additive statistics mean-preserving spread risk monotonicity finite moment variance

Cite

@article{arxiv.2608.10883,
  title  = {Two Moments for Risk-Monotone Additive Statistics},
  author = {Mark Whitmeyer},
  journal= {arXiv preprint arXiv:2608.10883},
  year   = {2026}
}