{
  "abstract": "Insurance pricing combines pooling with differentiation: a tariff may leave benchmark differences in expected loss partly mutualized or translate them into policy-level premium differences. We propose a benchmark-relative pooling--profiling scale with two complementary coordinates. The coupled $L^p$ coordinate measures policy-level alignment between an evaluated tariff and a stated benchmark pure premium, whereas the marginal Wasserstein coordinate compares their exposure-weighted premium distributions. The difference between their residual $p$-costs defines an allocation mismatch. Under portfolio balance, the coupled $L^1$ coordinate has an exact actuarial interpretation: it is the fraction of the transfer volume induced by full pooling that the tariff removes. Synthetic and motor-insurance applications show that broad classes, proxies, shrinkage and tail caps can affect marginal differentiation, policy-level allocation and transfers differently. A barycentric group-parity intervention further shows that conditional premium disparities can fall mainly through reallocation and restored benchmark-relative transfers, with little change in marginal differentiation.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.23294",
  "author_total": 2,
  "authors": [
    {
      "name": "Arthur Charpentier"
    },
    {
      "name": "Laurence Barry"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/266b1y4qjyvpc.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.23294",
  "fulltext_url": null,
  "id": "266b1y4qjyvpc",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.23294",
  "language": null,
  "licence": "CC-BY-NC-ND-4.0",
  "licence_label": "CC BY-NC-ND 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by-nc-nd/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "stat.AP"
    ],
    [
      "openalex",
      "1803|Probability and Risk Models"
    ]
  ],
  "openalex": "W7214029681",
  "pdf_url": "https://arxiv.org/pdf/2609.23294",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-20",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/266b1y4qjyvpc.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:23:33Z",
      "native_id": "2609.23294",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.23294"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:stat.AP",
      "subfield": "statistics"
    }
  ],
  "title": "Quantifying Portfolio Demutualization: A Benchmark-Relative Pooling--Profiling Scale",
  "title_text": "Quantifying Portfolio Demutualization: A Benchmark-Relative Pooling--Profiling Scale",
  "type": "preprint",
  "updated_at": "2026-10-30T12:23:33Z",
  "url": "https://research.draconitic.com/paper/266b1y4qjyvpc",
  "venue": "arXiv",
  "versions": []
}