{
  "abstract": "This paper is concerned with a stochastic optimal control problem under inside information. The control process depends on an $\\mathcal{F}_{T_0}$-measurable random variable $Y$, representing the static inside information, and is adapted to the enlarged filtration generated by the underlying Brownian motion and the random variable $Y$. Accordingly, the traditional stochastic integral fails to be well-defined in this non-adapted setting; we adopt forward integrals to formulate the stochastic integral terms in the system. By means of the Donsker delta function, the original controlled system is transformed into a $y$-parameterized system. We further establish the existence of solutions to forward \\textit{stochastic differential equations} (SDEs), and prove the uniqueness of solutions via flow transformation techniques. Under a Gaussian assumption on $Y$, we derive both necessary and sufficient optimality conditions for the aforementioned control problem. Subsequently, we formulate the \\textit{linear-quadratic} (LQ) optimal control problem under inside information. Through the $y$-parameterized transformation, the original problem is converted into an LQ control problem with random coefficients. A numerical example for the LQ case is provided at the end to validate our theoretical findings.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.02164",
  "author_total": 2,
  "authors": [
    {
      "name": "Yuxin Ye"
    },
    {
      "name": "Jingtao Shi"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/awxap2x51jrxq.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.02164",
  "fulltext_url": null,
  "id": "awxap2x51jrxq",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.02164",
  "language": null,
  "licence": "CC0-1.0",
  "licence_label": "CC0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/publicdomain/zero/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.OC"
    ],
    [
      "openalex",
      "2003|Stochastic processes and financial applications"
    ]
  ],
  "openalex": "W7207720516",
  "pdf_url": "https://arxiv.org/pdf/2609.02164",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-02",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/awxap2x51jrxq.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:18:20Z",
      "native_id": "2609.02164",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.02164"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.OC",
      "subfield": "optimisation-control"
    }
  ],
  "title": "Stochastic Optimal Control Problem under Inside Information",
  "title_text": "Stochastic Optimal Control Problem under Inside Information",
  "type": "preprint",
  "updated_at": "2026-10-30T12:18:20Z",
  "url": "https://research.draconitic.com/paper/awxap2x51jrxq",
  "venue": "arXiv",
  "versions": []
}