{
  "id": "2011.07341",
  "version": "v1",
  "published": "2020-11-14T17:10:46.000Z",
  "updated": "2020-11-14T17:10:46.000Z",
  "title": "Backward Volterra equations with time-changed Lévy noise and maximum principles",
  "authors": [
    "Giulia Di Nunno",
    "Michele Giordano"
  ],
  "categories": [
    "math.PR",
    "math.OC"
  ],
  "abstract": "We study an optimal control problem for Volterra type dynamics driven by time-changed L\\'evy noises with a maximum principle approach. For this we use different kind of information flows, the non anticipating stochastic derivative and we study backward Volterra integral equations (BSVIE) with time-change. We also provide an explicit solution for the linear BSVIEs. With these, we prove both a stochastic Pontryagin and Mangasarian maximum principle. We complete the work providing applications to optimal portfolio problems, particularly mean variance selection.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-11-14T17:10:46.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "maximum principle",
      "time-changed lévy noise",
      "backward volterra equations",
      "study backward volterra integral equations",
      "volterra type dynamics driven"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}