{
  "abstract": "We give an explicit solution to the five expert prediction with expert advice partial differential equation (PDE) in the finite-time horizon setting. The solution formula establishes that the adversary's rank strategy $(1,0,1,0,0)$ is globally optimal, and the COMB strategy $(1,0,1,0,1)$ is optimal exactly on the set where $x_1=x_2$ and $x_3=x_4$. The formula is derived from the solution of the geometric-stopping problem given in our companion paper through the transform principle of Bayraktar, Ekren and Zhang, which links the two problems by a Laplace transform. Inverting the transform term by term expresses the solution through a series of Gaussian and complementary error function kernels. The optimality of $(1,0,1,0,0)$ is reduced to the signs of $41$ one-variable Gaussian series, which are certified with computer assistance by Poisson summation, first-mode domination and interval arithmetic on $1616$ rational cells. The proofs of our main theorems, certificates included, are also formalized in the Lean proof assistant.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.38035",
  "author_total": 2,
  "authors": [
    {
      "name": "Jeff Calder"
    },
    {
      "name": "Nadejda Drenska"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/5ncj37e7kn45z.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.38035",
  "fulltext_url": null,
  "id": "5ncj37e7kn45z",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.38035",
  "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",
      "cs.GT"
    ],
    [
      "arxiv",
      "cs.LG"
    ],
    [
      "arxiv",
      "math.AP"
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      "arxiv",
      "math.OC"
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      "openalex",
      "2003|Stochastic processes and financial applications"
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  "openalex": "W7214926615",
  "pdf_url": "https://arxiv.org/pdf/2609.38035",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-29",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/5ncj37e7kn45z.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:25:35Z",
      "native_id": "2609.38035",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.38035"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.OC",
      "subfield": "optimisation-control"
    }
  ],
  "title": "The finite-horizon five-expert prediction problem",
  "title_text": "The finite-horizon five-expert prediction problem",
  "type": "preprint",
  "updated_at": "2026-10-30T12:25:35Z",
  "url": "https://research.draconitic.com/paper/5ncj37e7kn45z",
  "venue": "arXiv",
  "versions": []
}