{
  "abstract": "We study a two-regime summary of a real-valued loss distribution. The two representative levels and the boundary between them are chosen by minimizing a convex residual loss. When the distribution has an atom at the boundary, assigning that atom to the lower or upper regime can give different optimized costs. Taking the better whole-atom assignment yields the lower-semicontinuous cutoff profile. We prove epi-convergence of this profile under a loss-adapted \\(ψ\\)-weak topology and obtain convergence of minimum values and outer stability of optimal cutoff sets. Under a unique finite atom-free limiting cutoff, positive regime masses, and unique conditional centers, the two fitted levels and a canonical one-jump representation converge as well. We also examine the resulting summary from the viewpoint of monetary risk axioms, establish explicit failures of external monotonicity and subadditivity, and give finite-support algorithms with conditional error control. A four-scenario model illustrates the cutoff geometry and the role of ties and atoms.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.08821",
  "author_total": 2,
  "authors": [
    {
      "name": "Mihaela-Adriana Nistor"
    },
    {
      "name": "Ionel Popescu"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/65mrhez6656z2.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.08821",
  "fulltext_url": null,
  "id": "65mrhez6656z2",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.08821",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.PR"
    ],
    [
      "arxiv",
      "q-fin.RM"
    ],
    [
      "openalex",
      "1803|Risk and Portfolio Optimization"
    ]
  ],
  "openalex": "W7220986954",
  "pdf_url": "https://arxiv.org/pdf/2610.08821",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-01",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/65mrhez6656z2.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:27:42Z",
      "native_id": "2610.08821",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.08821"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.PR",
      "subfield": "probability"
    }
  ],
  "title": "Two-Regime Risk Measures under Convex Loss",
  "title_text": "Two-Regime Risk Measures under Convex Loss",
  "type": "preprint",
  "updated_at": "2026-10-30T12:27:42Z",
  "url": "https://research.draconitic.com/paper/65mrhez6656z2",
  "venue": "arXiv",
  "versions": []
}