By Law, Every Zero-Mean Risk Is the Difference of Two Equally Distributed Risks

Mark Whitmeyer

By Law, Every Zero-Mean Risk Is the Difference of Two Equally Distributed Risks

Theoretical Economics 2026-07-06 v1 Probability

Authors: Mark Whitmeyer

Abstract

We prove that every mean-zero probability law on the real line is the law of X-Y for some identically distributed real-valued random variables X and Y.

Cite

@article{arxiv.2607.05460,
  title  = {By Law, Every Zero-Mean Risk Is the Difference of Two Equally Distributed Risks},
  author = {Mark Whitmeyer},
  journal= {arXiv preprint arXiv:2607.05460},
  year   = {2026}
}