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PreprintCC BY 4.0arXiv

Weighted universal Value-at-Risk Superadditivity for discrete distributions

  • Alfred Müller
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Abstract

The concept of weighted universal Value-at-Risk superadditivity (WUVS) was recently introduced by Chen et al. (2026) as a generalization of the question whether for some infinite mean distributions convex combinations of i.i.d. random variables can stochastically dominate the parent distribution. In this short note we prove that the property WUVS can basically never hold for discrete distributions except for the case of comonotonicity. This implies as a corollary that for discrete distributions with infinite mean it can also never hold that convex combinations of i.i.d. random variables can stochastically dominate the parent distribution. This settles an open problem mentioned in Müller (2025).

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Cite

BibTeXRIS
BibTeX
@misc{muller2026weighted,
  title = {{Weighted universal Value-at-Risk Superadditivity for discrete distributions}},
  author = {Alfred Müller},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.26398},
  eprint = {2609.26398},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.26398},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - Weighted universal Value-at-Risk Superadditivity for discrete distributions
AU  - Alfred Müller
PY  - 2026
DA  - 2026/09/22
PB  - arXiv
DO  - 10.48550/arxiv.2609.26398
UR  - https://arxiv.org/abs/2609.26398
AB  - The concept of weighted universal Value-at-Risk superadditivity (WUVS) was recently introduced by Chen et al. (2026) as a generalization of the question whether for some infinite mean distributions convex combinations of i.i.d. random variables can stochastically dominate the parent distribution. In this short note we prove that the property WUVS can basically never hold for discrete distributions except for the case of comonotonicity. This implies as a corollary that for discrete distributions with infinite mean it can also never hold that convex combinations of i.i.d. random variables can stochastically dominate the parent distribution. This settles an open problem mentioned in Müller (2025).
ER  -