{
  "abstract": "This article studies a finite-horizon American put option with up to $m$ exercise rights under the risk-neutral Black--Scholes model, where consecutive exercises must be separated by a prescribed refractory period $δ>0$ and unused rights may expire. For each number of remaining rights, we show that optimal exercise is characterized by a single exercise boundary and that these boundaries are ordered by the number of remaining rights. We prove optimality of the first boundary-hitting time and establish local Lipschitz continuity of the exercise boundaries within each open deadline strip. Away from the deadlines, we derive smooth fit, the associated quasi-variational inequality and free-boundary formulation, an early-exercise-premium representation, recursive Volterra-type boundary equations, and a verification theorem. We also extend the recursive formulation to an independent random termination time, thereby allowing for exogenous termination of the option contract.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.30637",
  "author_total": 1,
  "authors": [
    {
      "name": "Katsunori Ano"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/6wac873fq676q.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.30637",
  "fulltext_url": null,
  "id": "6wac873fq676q",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.30637",
  "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.PR"
    ],
    [
      "arxiv",
      "q-fin.PR"
    ],
    [
      "openalex",
      "2003|Stochastic processes and financial applications"
    ]
  ],
  "openalex": "W7223262624",
  "pdf_url": "https://arxiv.org/pdf/2610.30637",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-22",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/6wac873fq676q.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:34:38Z",
      "native_id": "2610.30637",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.30637"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.PR",
      "subfield": "probability"
    }
  ],
  "title": "Multiple Stopping and Exercise Boundaries for American Put Options",
  "title_text": "Multiple Stopping and Exercise Boundaries for American Put Options",
  "type": "preprint",
  "updated_at": "2026-10-30T12:34:38Z",
  "url": "https://research.draconitic.com/paper/6wac873fq676q",
  "venue": "arXiv",
  "versions": []
}