{
  "id": "1612.03680",
  "version": "v1",
  "published": "2016-12-12T13:58:09.000Z",
  "updated": "2016-12-12T13:58:09.000Z",
  "title": "A note on conditional risk measures of Orlicz spaces and Orlicz-type modules",
  "authors": [
    "José Orihuela",
    "José Miguel Zapata"
  ],
  "categories": [
    "math.FA"
  ],
  "abstract": "We consider conditional and dynamic risk measures of Orlicz spaces and study their robust representation. For this purpose, given a probability space $(\\Omega,\\mathcal{E},\\PP)$, a sub-$\\sigma$-algebra $\\F$ of $\\mathcal{E}$, we study the relation between the classical Orlicz space $L^\\varphi(\\mathcal{E})$ and the modular Orlicz-type module $L^\\varphi_\\F(\\mathcal{E})$; based on conditional set theory, we describe the conditional order continuous dual of a Orlicz-type module; and by using scalarization and modular extensions of conditional risk measures together with elements of conditional set theory, we finally characterize the robust representation of conditional risk measures of Orlicz spaces.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-12-12T13:58:09.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "conditional risk measures",
      "orlicz space",
      "conditional set theory",
      "robust representation",
      "modular orlicz-type module"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}