{
  "id": "2207.03710",
  "version": "v1",
  "published": "2022-07-08T06:57:48.000Z",
  "updated": "2022-07-08T06:57:48.000Z",
  "title": "Non-linear Affine Processes with Jumps",
  "authors": [
    "Francesca Biagini",
    "Georg Bollweg",
    "Katharina Oberpriller"
  ],
  "comment": "30 pages",
  "categories": [
    "math.PR",
    "q-fin.MF"
  ],
  "abstract": "We present a probabilistic construction of $\\mathbb{R}^d$-valued non-linear affine processes with jumps. Given a set $\\Theta$ of affine parameters, we define a family of sublinear expectations on the Skorokhod space under which the canonical process $X$ is a (sublinear) Markov process with a non-linear generator. This yields a tractable model for Knightian uncertainty for which the sublinear expectation of a Markovian functional can be calculated via a partial integro-differential equation.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-07-08T06:57:48.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60G65",
      "60G07"
    ],
    "keywords": [
      "sublinear expectation",
      "valued non-linear affine processes",
      "partial integro-differential equation",
      "probabilistic construction",
      "affine parameters"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 30,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}