{
  "id": "1411.6256",
  "version": "v1",
  "published": "2014-11-23T16:06:49.000Z",
  "updated": "2014-11-23T16:06:49.000Z",
  "title": "On robust representation of conditional risk measures on a $L^\\infty$-type module",
  "authors": [
    "José Miguel Zapata"
  ],
  "categories": [
    "math.FA",
    "q-fin.RM"
  ],
  "abstract": "The purpose of this paper is to establish a robust representation theorem for conditional risk measures by using a module-based convex analysis, where risk measures are defined on a $L^\\infty$-type module. We define and study a Fatou property for this kind of risk measures, which is a generalization of the already known Fatou property for static risk measures. In order to prove this robust representation theorem we provide a modular version of Krein-Smulian theorem.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-11-23T16:06:49.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "conditional risk measures",
      "type module",
      "robust representation theorem",
      "fatou property",
      "static risk measures"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1411.6256Z"
    }
  }
}