{
  "abstract": "Let X be a spectrally negative Lévy process observed up to an inde- pendent exponential time T with parameter γ > 0. We study the joint law of the maximum drawdown and the maximum drawup of X on [0, T ]. The path is decomposed according to the two possible orderings of its in- fimum and supremum. Conditional on the values of these extrema and on their ordering, the resulting pre-, intermediate, and post- components are independent. We identify their laws as Doob h-transforms of killed spec- trally negative Lévy processes and express the corresponding distribution functions explicitly in terms of the γ-scale functions W (γ) and Z(γ) and their derivatives. Combining the conditional laws with the joint densities of the extrema yields integral representations of the joint distribution and moments.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.03634",
  "author_total": 2,
  "authors": [
    {
      "name": "Ceren Vardar Acar"
    },
    {
      "name": "Emre Akdogan"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/8tww3pkdn9g7x.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.03634",
  "fulltext_url": null,
  "id": "8tww3pkdn9g7x",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.03634",
  "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",
      "1803|Probability and Risk Models"
    ]
  ],
  "openalex": "W7208788585",
  "pdf_url": "https://arxiv.org/pdf/2609.03634",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-03",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/8tww3pkdn9g7x.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:18:36Z",
      "native_id": "2609.03634",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.03634"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.PR",
      "subfield": "probability"
    }
  ],
  "title": "Joint Laws of Maximum Drawdown and Maximum Drawup for Spectrally Negative Lévy Processes",
  "title_text": "Joint Laws of Maximum Drawdown and Maximum Drawup for Spectrally Negative Lévy Processes",
  "type": "preprint",
  "updated_at": "2026-10-30T12:18:36Z",
  "url": "https://research.draconitic.com/paper/8tww3pkdn9g7x",
  "venue": "arXiv",
  "versions": []
}