Separation Theorems for Increasing Convex and Weak 3-Convex Orders on Real-Valued Random Variables

@misc{su2026separation,
  title = {{Separation Theorems for Increasing Convex and Weak 3-Convex Orders on Real-Valued Random Variables}},
  author = {Yuting Su and Meng Guan and Zhenfeng Zou and Taizhong Hu},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.37025},
  eprint = {2610.37025},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.37025},
}

TY  - UNPB
TI  - Separation Theorems for Increasing Convex and Weak 3-Convex Orders on Real-Valued Random Variables
AU  - Yuting Su
AU  - Meng Guan
AU  - Zhenfeng Zou
AU  - Taizhong Hu
PY  - 2026
DA  - 2026/10/27
PB  - arXiv
DO  - 10.48550/arxiv.2610.37025
UR  - https://arxiv.org/abs/2610.37025
AB  - We examine separation theorems for the increasing convex (stop-loss) order and weak 3-convex order. We improve prior proofs for the increasing convex order by using integrated survival functions. We extend the separation theorem for weak 3-convex order from non-negative random variables to general real-valued random variables with finite second moments via a constructive approach based on higher-order integrated survival functions. A counterexample verifies that the $3$-convex order and $2$-convex order chain does not hold for the weak $3$-convex order. Our results enrich stochastic order theories for actuarial science and risk management.
ER  -