{
  "abstract": "Expectiles are the only law-invariant risk measures that are both coherent and elicitable. Unlike Conditional Value-at-Risk (CVaR), however, they do not admit a Rockafellar--Uryasev representation that admits tractable Wasserstein reformulations. We address this difficulty by developing an envelope theorem for worst-case expectiles that characterizes the worst-case expectile over a Wasserstein ambiguity set as the unique root of a worst-case expectation with a two-piece affine integrand. This representation permits direct application of standard Wasserstein duality. Using this result, we reformulate a multi-period tri-level mean--expectile portfolio problem as four parametric linear programs with constraints. We establish four structural properties of the proposed model: an endogenously damped price of robustness, a decision-dependent critical radius beyond which the expectile tail component becomes inactive, exact recovery of the nominal model at zero ambiguity, and a characterization of how the Wasserstein ground metric determines whether the limiting portfolio becomes more concentrated or more diversified. Numerical experiments on 90 FTSE constituents over 3,341 out-of-sample trading days show that the expectile model outperforms a CVaR model matched on ambiguity set, radius, ground metric, and trade-off weight in all nine parameter cells---significantly so whenever the radius is non-trivial. The experiments further confirm the predicted degeneracy under the ground metric.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.11917",
  "author_total": 2,
  "authors": [
    {
      "name": "Rupendra Yadav"
    },
    {
      "name": "Aparna Mehra"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/f329safan7ch2.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.11917",
  "fulltext_url": null,
  "id": "f329safan7ch2",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.11917",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.OC"
    ],
    [
      "arxiv",
      "q-fin.CP"
    ],
    [
      "openalex",
      "1803|Risk and Portfolio Optimization"
    ]
  ],
  "openalex": "W7221140626",
  "pdf_url": "https://arxiv.org/pdf/2610.11917",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-08",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/f329safan7ch2.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:27:58Z",
      "native_id": "2610.11917",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.11917"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.OC",
      "subfield": "optimisation-control"
    }
  ],
  "title": "Multi-period Mean-Expectile Portfolio Optimization under Wasserstein Ambiguity: Reformulation, Degeneracy and the Role of the Ground Metric",
  "title_text": "Multi-period Mean-Expectile Portfolio Optimization under Wasserstein Ambiguity: Reformulation, Degeneracy and the Role of the Ground Metric",
  "type": "preprint",
  "updated_at": "2026-10-30T12:27:58Z",
  "url": "https://research.draconitic.com/paper/f329safan7ch2",
  "venue": "arXiv",
  "versions": []
}