{
  "annotation_id": "37806396-c64f-4f38-989d-d5766742e055",
  "date_created": "2026-03-02T18:00:43.220000Z",
  "date_modified": "2026-03-02T18:00:43.220000Z",
  "file_hash": "1d3e8f07061fa34549f995ab4e392844b37be09a87fa514459a664763531d227",
  "private": false,
  "record": {
    "abstract": "Using a family of modified Weibull distributions, encompassing both\nsub-exponentials and super-exponentials, to parameterize the marginal\ndistributions of asset returns and their multivariate generalizations with\nGaussian copulas, we offer exact formulas for the tails of the distribution\n$P(S)$ of returns $S$ of a portfolio of arbitrary composition of these assets.\nWe find that the tail of $P(S)$ is also asymptotically a modified Weibull\ndistribution with a characteristic scale $\\chi$ function of the asset weights\nwith different functional forms depending on the super- or sub-exponential\nbehavior of the marginals and on the strength of the dependence between the\nassets. We then treat in details the problem of risk minimization using the\nValue-at-Risk and Expected-Shortfall which are shown to be (asymptotically)\nequivalent in this framework.",
    "arxiv_id": "physics/0301009",
    "authors": [
      "Y. Malevergne",
      "D. Sornette"
    ],
    "categories": [
      "physics.soc-ph",
      "physics.gen-ph",
      "q-fin.RM"
    ],
    "doi": "10.1088/1469-7688/4/1/002",
    "journal_ref": "Quantitative Finance 4 (1), 17-36 (2003)",
    "title": "VaR-Efficient Portfolios for a Class of Super- and Sub-Exponentially   Decaying Assets Return Distributions",
    "url": "https://arxiv.org/abs/physics/0301009"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "2834cbdd-c2b7-4957-a9a3-f3b7273f24f1",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}