{
  "abstract": "Paid triangles identify some components of reserve uncertainty while others enter through modelling assumptions. We distinguish population identification, recovery by free accident-year-level and two-stage second-moment fits, and precision at practical triangle sizes. In a compound frequency--severity hierarchy, the population law identifies the row dispersion governing non-diversifying reserve variance. With one free level per accident year, its profile likelihood attains its supremum only at homogeneity: the levels absorb realised row heterogeneity on every triangle, in amounts and in counts. Anchoring reopens this channel, but supplies only one observation per accident year. On a $10 \\times 10$ triangle the anchored estimate remains uncertain by a factor of several. Within-row allocation dispersion survives conditioning on row totals and hence survives free levels. In the predictive experiments, the treatment of mean-structure estimation error separated the procedures by several times more than the choice among plausible variance laws. A law of the correct form improved coverage only when its dispersion came from a prior instead of the free-level fit. On an outcome-free Schedule~P panel, no amount-only procedure approaches nominal coverage. Strongly one-sided misses reveal a displacement of realised reserves relative to the fitted predictive centres that changing the amount-only variance law cannot repair.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.41087",
  "author_total": 1,
  "authors": [
    {
      "name": "Robin Van Oirbeek"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/4ve68jvdwqqyt.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.41087",
  "fulltext_url": null,
  "id": "4ve68jvdwqqyt",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.41087",
  "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",
      "stat.ME"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2610.41087",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-30",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/4ve68jvdwqqyt.ris",
  "sources": [
    {
      "first_seen": "2026-11-02T12:21:25Z",
      "native_id": "2610.41087",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.41087"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:stat.ME",
      "subfield": "statistics"
    }
  ],
  "title": "What Paid Triangles Identify about Reserve Uncertainty: Information Boundaries in Loss Reserving",
  "title_text": "What Paid Triangles Identify about Reserve Uncertainty: Information Boundaries in Loss Reserving",
  "type": "preprint",
  "updated_at": "2026-11-04T15:20:53Z",
  "url": "https://research.draconitic.com/paper/4ve68jvdwqqyt",
  "venue": "arXiv",
  "versions": []
}