{
  "abstract": "In incomplete markets, no-arbitrage (NFLVR) guarantees the existence, not the uniqueness, of an equivalent local martingale measure (ELMM): unhedgeable risks (jumps, stochastic volatility) admit a whole family of equivalent measures, and asset dynamics alone cannot pin down the one the market selects. We characterize the identifiability of $Q$ from option data and propose a measure that is identifiable from data yet prices any claim consistently. The key boundary is an ``identification wall'': European options identify only the terminal marginal, while out-of-sample tails and path/joint structure require instruments matched to the priced risk (variance or higher-moment swaps, path-dependent claims). Within this view, minimum-relative-entropy weighted Monte Carlo (WMC) is the optimal baseline for the marginal; we generalize it to a full path-space measure change parameterized by a neural network on physical scenarios---XiNet---which learns $ξ=\\mathrm{d}\\mathbb{Q}/\\mathrm{d}\\mathbb{P}$ directly from 8 model-free path features, with option prices as a soft constraint. On European (marginal) pricing XiNet matches but does not surpass WMC, and both are bound by the identification wall out-of-sample. On path-dependent claims the picture reverses: calibrated on the same European surface, per-marginal methods fail structurally (an ATM forward-start is mispriced by $\\sim+100\\%$), whereas XiNet's single self-consistent measure keeps the bias to $+0.3\\%$, beating maximum-entropy WMC ($-24\\%$), because $ξ=f_θ(\\text{path features})$ captures joint structure Europeans cannot constrain. Identification is thus risk-specific, and XiNet is a single measure that absorbs available instruments and prices all claims consistently.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.01941",
  "author_total": 2,
  "authors": [
    {
      "name": "Ziyuan Zhang"
    },
    {
      "name": "Kiseop Lee"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/bc4sk1ncsekkr.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.01941",
  "fulltext_url": null,
  "id": "bc4sk1ncsekkr",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.01941",
  "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.AP"
    ],
    [
      "openalex",
      "2003|Stochastic processes and financial applications"
    ]
  ],
  "openalex": "W7207859655",
  "pdf_url": "https://arxiv.org/pdf/2609.01941",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-01",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/bc4sk1ncsekkr.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:18:26Z",
      "native_id": "2609.01941",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.01941"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:stat.AP",
      "subfield": "statistics"
    }
  ],
  "title": "Neural Networks Learning the Radon--Nikodym Derivative: Empirical Option Pricing in Incomplete Markets",
  "title_text": "Neural Networks Learning the Radon--Nikodym Derivative: Empirical Option Pricing in Incomplete Markets",
  "type": "preprint",
  "updated_at": "2026-10-30T12:18:26Z",
  "url": "https://research.draconitic.com/paper/bc4sk1ncsekkr",
  "venue": "arXiv",
  "versions": []
}