{
  "abstract": "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.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.37025",
  "author_total": 4,
  "authors": [
    {
      "name": "Yuting Su"
    },
    {
      "name": "Meng Guan"
    },
    {
      "name": "Zhenfeng Zou"
    },
    {
      "name": "Taizhong Hu"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/75khzv9x2r077.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.37025",
  "fulltext_url": null,
  "id": "75khzv9x2r077",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.37025",
  "language": null,
  "licence": "LicenseRef-arXiv-nonexclusive-1.0",
  "licence_label": "arXiv licence",
  "licence_source": "article",
  "licence_url": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.PR"
    ],
    [
      "openalex",
      "1803|Probability and Risk Models"
    ]
  ],
  "openalex": "W7224137827",
  "pdf_url": "https://arxiv.org/pdf/2610.37025",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-27",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/75khzv9x2r077.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:35:53Z",
      "native_id": "2610.37025",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.37025"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.PR",
      "subfield": "probability"
    }
  ],
  "title": "Separation Theorems for Increasing Convex and Weak 3-Convex Orders on Real-Valued Random Variables",
  "title_text": "Separation Theorems for Increasing Convex and Weak 3-Convex Orders on Real-Valued Random Variables",
  "type": "preprint",
  "updated_at": "2026-10-30T12:35:53Z",
  "url": "https://research.draconitic.com/paper/75khzv9x2r077",
  "venue": "arXiv",
  "versions": []
}