{
  "abstract": "This paper investigates the cumulative prospect theory (CPT)-based shortfall risk measure where the value (utility) function and the distortion (probability weighting) functions are ambiguous. We propose a worst-case CPT-based shortfall risk measure where the capital requirement is based on the worst-case value function and distortion functions from an ambiguity set constructed with user-specific information (e.g., preference between risky and certain lotteries) and well-known general information such as the S-shape of the value functions. When the underlying random loss is discretely distributed and parameters in pairs of lotteries remain undetermined, we demonstrate that the worst-case value function and the distortion functions have a piecewise linear structure. Based on this observation, we develop an adaptive preference elicitation approach extended from the well-known polyhedral method to simultaneously elicit the distortion functions and the positive and negative parts of the value function by solving a sequence of mixed-integer linear programs. Based on the elicited distortions, we design new queries to construct a feasible set of the holistic value functions. The proposed framework iteratively shrinks the ambiguity set through designed queries, yielding a computationally implementable robust CPT-based shortfall risk measure. To examine the in-sample and out-of-sample performance of the elicited CPT-based preference functions and the resulting preference robust shortfall risk measure, we conduct numerical experiments under an S-shaped value function and inverse S-shaped distortion functions and report the corresponding results.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2611.02059",
  "author_total": 3,
  "authors": [
    {
      "name": "Sainan Zhang"
    },
    {
      "name": "Erick Delage"
    },
    {
      "name": "Huifu Xu"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/fjx3m8tqy41dw.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2611.02059",
  "fulltext_url": null,
  "id": "fjx3m8tqy41dw",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2611.02059",
  "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"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2611.02059",
  "pmcid": null,
  "pmid": null,
  "published": "2026-11-01",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/fjx3m8tqy41dw.ris",
  "sources": [
    {
      "first_seen": "2026-11-03T12:21:10Z",
      "native_id": "2611.02059",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2611.02059"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.OC",
      "subfield": "optimisation-control"
    }
  ],
  "title": "Adaptive Preference Elicitation in Preference Robust CPT-Based Shortfall",
  "title_text": "Adaptive Preference Elicitation in Preference Robust CPT-Based Shortfall",
  "type": "preprint",
  "updated_at": "2026-11-05T15:20:22Z",
  "url": "https://research.draconitic.com/paper/fjx3m8tqy41dw",
  "venue": "arXiv",
  "versions": []
}