{
  "id": "1509.07081",
  "version": "v1",
  "published": "2015-09-23T18:14:37.000Z",
  "updated": "2015-09-23T18:14:37.000Z",
  "title": "On conditional Lebesgue property for conditional risk measures",
  "authors": [
    "José Orihuela",
    "José Miguel Zapata"
  ],
  "categories": [
    "math.FA"
  ],
  "abstract": "In this paper we first carry out a study of the connection between the notion of locally $L^0$-convex modules, the analytic basis of the conditional risk measures, and the notion of conditional locally convex spaces. Second, we provide a conditional version of the classical James' Theorem of characterization of weak compactness. Finally, as application of the developed theory we stablish a version of the so-known Jouini-Schachermayer-Touzi Theorem for robust representation of conditional $L^0$-convex risk measures defined on a $L^\\infty$-type module with the conditional Lebesgue property.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-09-23T18:14:37.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "conditional risk measures",
      "conditional lebesgue property",
      "convex risk measures",
      "so-known jouini-schachermayer-touzi theorem",
      "conditional locally convex spaces"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2015arXiv150907081O"
    }
  }
}