{
  "id": "1301.3798",
  "version": "v3",
  "published": "2013-01-16T19:46:28.000Z",
  "updated": "2014-09-04T17:42:43.000Z",
  "title": "Root's barrier, viscosity solutions of obstacle problems and reflected FBSDEs",
  "authors": [
    "Harald Oberhauser",
    "Goncalo dos Reis"
  ],
  "categories": [
    "math.PR",
    "math.AP"
  ],
  "abstract": "We revisit work of Rost, Dupire and Cox--Wang on connections between Root's solution of the Skorokhod embedding problem and obstacle problems. We develop an approach based on viscosity sub- and supersolutions and an accompanying comparison principle. This gives a complete characterization of (reversed) Root barriers and also leads to new proofs of existence as well as minimality of such barrier solutions by pure PDE methods. The approach is self-contained and general enough to cover martingale diffusions with degenerate elliptic or time-dependent volatility; it also provides insights about the dynamics of general Skorokhod embeddings.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2014-07-22T17:44:18.000Z",
      "abstract": "We revisit work of Dupire and Cox--Wang on connections between Root's solution and obstacle problems and develop an approach based on viscosity sub- and supersolutions and the comparison principle. This leads to new proofs of existence as well as minimality of a Root solution by pure PDE methods. The approach is self-contained and general enough to cover martingale diffusions with degenerate elliptic and time-dependent volatility; it also provides insights about the dynamics of general Skorokhod embeddings by identifying them as supersolutions.",
      "comment": null,
      "journal": null,
      "doi": null
    },
    {
      "version": "v3",
      "updated": "2014-09-04T17:42:43.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "obstacle problems",
      "viscosity solutions",
      "roots barrier",
      "reflected fbsdes",
      "general skorokhod embeddings"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1301.3798G"
    }
  }
}