{
  "abstract": "An optimal stopping problem is monotone when its stopping region is preserved under subsequent transitions, so that the one-step look-ahead stopping time is optimal. We develop a finite-horizon discrete-time theory of multiple stopping that separates general recursive dynamic programming from this stronger monotone structure. Extending the classical martingale-system approach, we construct a recursively defined optimal vector of stopping times without assuming monotonicity. If monotonicity holds at every exercise level, this vector coincides with the recursive vector of one-step look-ahead stopping times. A bounded counterexample shows that monotonicity of the original single-stopping problem alone is insufficient, whereas monotonicity propagates to every level when the level-one one-step look-ahead function is deterministic. We apply the theory to multiple-selection last-success problems. For the classical independent odds setting, a continuous-time Poisson embedding gives an alternative proof of the multiple-stopping lower bound and clarifies the associated threshold constants. We also examine random horizons, Markov-dependent trials, and an unknown success probability",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.10237",
  "author_total": 1,
  "authors": [
    {
      "name": "Katsunori Ano"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/feqbrqayxqce3.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.10237",
  "fulltext_url": null,
  "id": "feqbrqayxqce3",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.10237",
  "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"
    ],
    [
      "openalex",
      "1705|Optimization and Search Problems"
    ]
  ],
  "openalex": "W7220944327",
  "pdf_url": "https://arxiv.org/pdf/2610.10237",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-07",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/feqbrqayxqce3.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:27:42Z",
      "native_id": "2610.10237",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.10237"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.PR",
      "subfield": "probability"
    }
  ],
  "title": "Monotone Multiple Stopping and Last-Success Problems",
  "title_text": "Monotone Multiple Stopping and Last-Success Problems",
  "type": "preprint",
  "updated_at": "2026-10-30T12:27:42Z",
  "url": "https://research.draconitic.com/paper/feqbrqayxqce3",
  "venue": "arXiv",
  "versions": []
}