{
  "abstract": "We study adapted finite-variation tracking of fractional Brownian motion under quadratic loss and proportional adjustment costs. For $H\\in(0,1)$, \\[ V_λ(T;a,b,σ)\\underset{λ\\downarrow0}{\\sim}κ_HT a^{(1-H)/(1+H)}(λb)^{2H/(1+H)}σ^{2/(1+H)}. \\] The positive long-run cell value $κ_H$ is unchanged by full past information. A bounded full-past reset correction yields finite-horizon bounds and continuity in $H$. The Brownian value is $κ_{1/2}=\\frac12(\\frac32)^{2/3}$. Coupling local paths with their filtrations gives a local limit, which we verify for Gaussian Volterra targets. Every asymptotically optimal control has the same leading tracking--variation cost split. Primal and dual bounds quantify the cell value. For $H<1/2$, we construct a positive-factor approximation and relate factor resolution to horizon length.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2611.01727",
  "author_total": 1,
  "authors": [
    {
      "name": "Alexandre Autran"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/059x74179x308.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2611.01727",
  "fulltext_url": null,
  "id": "059x74179x308",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2611.01727",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.OC"
    ],
    [
      "arxiv",
      "math.PR"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2611.01727",
  "pmcid": null,
  "pmid": null,
  "published": "2026-11-01",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/059x74179x308.ris",
  "sources": [
    {
      "first_seen": "2026-11-03T12:21:10Z",
      "native_id": "2611.01727",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2611.01727"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.OC",
      "subfield": "optimisation-control"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.PR",
      "subfield": "probability"
    }
  ],
  "title": "Singular Tracking of Fractional Brownian Motion under Proportional Costs",
  "title_text": "Singular Tracking of Fractional Brownian Motion under Proportional Costs",
  "type": "preprint",
  "updated_at": "2026-11-05T15:20:22Z",
  "url": "https://research.draconitic.com/paper/059x74179x308",
  "venue": "arXiv",
  "versions": []
}