{
  "id": "1902.06780",
  "version": "v1",
  "published": "2019-02-18T20:02:46.000Z",
  "updated": "2019-02-18T20:02:46.000Z",
  "title": "Expansion of a filtration with a stochastic process: the information drift",
  "authors": [
    "Léo Neufcourt",
    "Philip Protter"
  ],
  "categories": [
    "math.PR"
  ],
  "abstract": "When expanding a filtration with a stochastic process it is easily possible for semimartingale no longer to remain semimartingales in the enlarged filtration. Y. Kchia and P. Protter indicated a way to avoid this pitfall in 2015, but they were unable to give the semimartingale decomposition in the enlarged filtration except for special cases. We provide a way to compute such a decomposition, and moreover we provide a sufficient condition for It\\^o processes to remain It\\^o processes in the enlarged filtration. This has significance in applications to Mathematical Finance.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-02-18T20:02:46.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60G07",
      "60G48",
      "60G35",
      "91G80"
    ],
    "keywords": [
      "stochastic process",
      "information drift",
      "enlarged filtration",
      "remain semimartingales",
      "special cases"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}