{
  "abstract": "We study the worst-case relative growth rate of a fixed functionally generated portfolio under restrictions on market-weight dynamics over a compact convex market state space. For a nonempty compact forward shift-invariant path family, the pathwise wealth decomposition identifies the global rate with the minimum invariant average of the one-step $L$-divergence. For paths generated by a compact one-step transition relation, this rate is also the minimum over balanced transition measures, and a minimizing measure can be chosen on one relation basic set. For a fixed initial state, we study the lower limit of the minimum average $L$-divergence over the first $t$ periods as $t\\to\\infty$. We represent this value using empirical transition laws generated from that state. Their common state marginals are supported on chain-recurrent states that are chain-accessible from the initial state. The lower bound is obtained by minimizing the average $L$-divergence over balanced transition measures on chain-accessible basic sets. Finite exact reachability gives an upper bound. Examples show that both bounds can be strict. We also give a finite exact reachability condition under which the minimum average $L$-divergence over the first $t$ periods converges for paths confined to a basic set.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.41603",
  "author_total": 2,
  "authors": [
    {
      "name": "Jilong Xu"
    },
    {
      "name": "Xiaojun Cui"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/efz7rt6c9df81.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.41603",
  "fulltext_url": null,
  "id": "efz7rt6c9df81",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.41603",
  "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.DS"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2610.41603",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-30",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/efz7rt6c9df81.ris",
  "sources": [
    {
      "first_seen": "2026-11-02T12:21:20Z",
      "native_id": "2610.41603",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.41603"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.DS",
      "subfield": "dynamical-systems"
    }
  ],
  "title": "Worst-Case Relative Growth of Functionally Generated Portfolios under Restricted Market-Weight Dynamics",
  "title_text": "Worst-Case Relative Growth of Functionally Generated Portfolios under Restricted Market-Weight Dynamics",
  "type": "preprint",
  "updated_at": "2026-11-04T15:20:52Z",
  "url": "https://research.draconitic.com/paper/efz7rt6c9df81",
  "venue": "arXiv",
  "versions": []
}