{
  "abstract": "We study infinite-horizon discounted mean field control of finite-state continuous-time Markov chains with unbounded transition rates and a relative-entropy rate penalty. Under mild assumptions, the value function is the unique bounded viscosity solution of the stationary Hamilton--Jacobi--Bellman equation on the closed probability simplex. Joint convexity of a quadratically corrected flux Lagrangian and smoothness of the data yield global semiconvexity, intrinsic $\\mathcal{C}^{1,1}$ regularity, and optimal Gibbs feedback. For positive symmetric reference rates, an entropy-plus-value free energy gives global exponential convergence under a quantitative curvature condition. We also establish inverse-temperature limits for values and, under parameter-uniform hypotheses, for feedbacks and closed-loop trajectories. With population-independent reference rates and a potential state-cost structure, optimal planner trajectories induce discounted finite-state mean field game equilibria. As an application, size-dependent market-making quotes with exponential demand admit an exact revenue-to-entropy reformulation; a convex inventory-crowding potential connects optimal quoting to stabilization of the inventory distribution.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.24883",
  "author_total": 2,
  "authors": [
    {
      "name": "Asaf Cohen"
    },
    {
      "name": "Aditya Priya"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/2xht99dtxajyk.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.24883",
  "fulltext_url": null,
  "id": "2xht99dtxajyk",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.24883",
  "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": "W7222997674",
  "pdf_url": "https://arxiv.org/pdf/2610.24883",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-17",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/2xht99dtxajyk.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:30:57Z",
      "native_id": "2610.24883",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.24883"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.OC",
      "subfield": "optimisation-control"
    }
  ],
  "title": "Entropy-Regularized Finite-State Mean Field Control: Regularity and Stability",
  "title_text": "Entropy-Regularized Finite-State Mean Field Control: Regularity and Stability",
  "type": "preprint",
  "updated_at": "2026-10-30T12:33:44Z",
  "url": "https://research.draconitic.com/paper/2xht99dtxajyk",
  "venue": "arXiv",
  "versions": []
}