{
  "abstract": "We study simple predictable processes whose coefficients are represented by neural networks. On finite measure spaces, we establish density results for neural networks in Orlicz spaces. For filtrations generated by a stochastic process, measurable random variables, including at stopping times, can be approximated by neural networks depending on finitely many observations. Every stochastic integral with respect to a semimartingale can then be approximated, in the semimartingale topology, by integrals of such simple predictable processes. We show that restricting trading strategies to this class leaves the minimal mean-variance hedging error under partial information unchanged and obtain a no-free-lunch characterization in terms of equivalent martingale measures. Finally, the Bichteler-Dellacherie characterization of semimartingales remains valid even upon restricting the predictable integrands to those whose coefficients are represented by neural networks.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.31578",
  "author_total": 2,
  "authors": [
    {
      "name": "Aleksandar Arandjelovic"
    },
    {
      "name": "Uwe Schmock"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/7k1p12wbvxjhe.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.31578",
  "fulltext_url": null,
  "id": "7k1p12wbvxjhe",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.31578",
  "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"
    ],
    [
      "openalex",
      "2003|Stochastic processes and financial applications"
    ]
  ],
  "openalex": "W7214658848",
  "pdf_url": "https://arxiv.org/pdf/2609.31578",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-25",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/7k1p12wbvxjhe.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:24:57Z",
      "native_id": "2609.31578",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.31578"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.PR",
      "subfield": "probability"
    }
  ],
  "title": "Algorithmic trading and stochastic integration",
  "title_text": "Algorithmic trading and stochastic integration",
  "type": "preprint",
  "updated_at": "2026-10-30T12:24:57Z",
  "url": "https://research.draconitic.com/paper/7k1p12wbvxjhe",
  "venue": "arXiv",
  "versions": []
}