{
  "abstract": "This paper concerns the variational inequality arising from a specific singular control problem: portfolio selection under proportional transaction costs. This variational inequality is a gradient-constrained partial differential equation (PDE). Generally, the literature only guarantees the W^{2, \\infty} regularity of the solution to such a PDE, and counterexamples exist for higher regularity. In this paper, by exploiting the concavity of the value function, we connect this gradient-constrained problem to an obstacle problem, and finally show that the solution is C^{2,α} except at the corner points where multiple gradient constraints bind. Especially, if there are two assets, then a global C^{2,α} solution can be guaranteed.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.23028",
  "author_total": 2,
  "authors": [
    {
      "name": "Xinfu Chen"
    },
    {
      "name": "Shuaijie Qian"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/1v4tg420bbkyp.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.23028",
  "fulltext_url": null,
  "id": "1v4tg420bbkyp",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.23028",
  "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.OC"
    ],
    [
      "openalex",
      "2003|Stochastic processes and financial applications"
    ]
  ],
  "openalex": "W7213996525",
  "pdf_url": "https://arxiv.org/pdf/2609.23028",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-29",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/1v4tg420bbkyp.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:36:32Z",
      "native_id": "2609.23028",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.23028"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.OC",
      "subfield": "optimisation-control"
    }
  ],
  "title": "Regularity of the Value Function in Multi-Asset Portfolio Selection with Proportional Transaction Costs",
  "title_text": "Regularity of the Value Function in Multi-Asset Portfolio Selection with Proportional Transaction Costs",
  "type": "preprint",
  "updated_at": "2026-11-01T12:20:50Z",
  "url": "https://research.draconitic.com/paper/1v4tg420bbkyp",
  "venue": "arXiv",
  "versions": []
}