{
  "abstract": "We study equilibrium and risk evaluation in large sparse economic networks with heterogeneous responses, shocks, and bilateral exposures. Our approach approximates the distribution of equilibrium outcomes through local computations on a limiting rooted network. Under marked local weak convergence, we prove convergence in probability of the empirical equilibrium distribution in two settings: uniformly contractive responses and bounded monotone nonexpansive responses whose lower and upper root iterations coalesce. In the latter setting, the limit is independent of the measurable finite-network equilibrium selection, even when equilibria are not unique. Under bounded domain and continuity assumptions, this convergence extends to law-invariant risk measures, including conditional value-at-risk, with recursion-depth error bounds under additional regularity. Numerical experiments on production networks and payment clearing systems illustrate the accuracy and computational benefits of the local approximation.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.27107",
  "author_total": 2,
  "authors": [
    {
      "name": "Hamed Amini"
    },
    {
      "name": "Zhecheng Wu"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/fmkf4h1t482n3.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.27107",
  "fulltext_url": null,
  "id": "fmkf4h1t482n3",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.27107",
  "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"
    ],
    [
      "arxiv",
      "q-fin.MF"
    ],
    [
      "arxiv",
      "q-fin.RM"
    ],
    [
      "openalex",
      "2002|Economic theories and models"
    ]
  ],
  "openalex": "W7214219300",
  "pdf_url": "https://arxiv.org/pdf/2609.27107",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-22",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/fmkf4h1t482n3.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:24:00Z",
      "native_id": "2609.27107",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.27107"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.PR",
      "subfield": "probability"
    }
  ],
  "title": "Local Weak Limits for Equilibrium and Risk in Economic Networks",
  "title_text": "Local Weak Limits for Equilibrium and Risk in Economic Networks",
  "type": "preprint",
  "updated_at": "2026-10-30T12:24:00Z",
  "url": "https://research.draconitic.com/paper/fmkf4h1t482n3",
  "venue": "arXiv",
  "versions": []
}