{
  "abstract": "Mitigating \\emph{drawdown}, the decline in wealth from its running peak, presents a canonical problem in path-dependent risk control. In this paper, we develop a finite-horizon control framework that enforces a prescribed maximum percentage drawdown limit in multi-asset stochastic systems. Our first result is an exact robust-invariance theorem characterizing every control action that preserves a prescribed drawdown limit against all supported returns. We show that every robustly safe control admits a \\emph{drawdown-modulated} form: the product of the current drawdown \\emph{cushion} and a feasible \\emph{normalized direction}. This yields a complete parameterization of robustly drawdown-safe policies. Additionally, under stagewise-independent returns, we show that optimizing over all robustly safe causal policies reduces to a one-dimensional Bellman recursion and yields an optimal robustly safe state-feedback policy. Finally, we characterize the linear time-invariant (LTI) gains satisfying a prescribed drawdown limit and prove that optimal drawdown modulation achieves no lower expected return under the same limit. Strict expected-return improvement holds for horizons of at least two stages whenever the LTI policy has positive expected one-stage net return.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.23272",
  "author_total": 1,
  "authors": [
    {
      "name": "Chung-Han Hsieh"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/9hm4pe2k80ppg.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.23272",
  "fulltext_url": null,
  "id": "9hm4pe2k80ppg",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.23272",
  "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"
    ],
    [
      "arxiv",
      "q-fin.MF"
    ],
    [
      "arxiv",
      "q-fin.RM"
    ],
    [
      "openalex",
      "1803|Risk and Portfolio Optimization"
    ]
  ],
  "openalex": "W7214003134",
  "pdf_url": "https://arxiv.org/pdf/2609.23272",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-20",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/9hm4pe2k80ppg.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:23:27Z",
      "native_id": "2609.23272",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.23272"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.OC",
      "subfield": "optimisation-control"
    }
  ],
  "title": "On Control of Drawdown: Robust Invariance and Optimality",
  "title_text": "On Control of Drawdown: Robust Invariance and Optimality",
  "type": "preprint",
  "updated_at": "2026-10-30T12:23:27Z",
  "url": "https://research.draconitic.com/paper/9hm4pe2k80ppg",
  "venue": "arXiv",
  "versions": []
}