{
  "id": "1105.2973",
  "version": "v4",
  "published": "2011-05-15T21:54:48.000Z",
  "updated": "2011-12-12T09:43:41.000Z",
  "title": "On backward stochastic differential equations and strict local martingales",
  "authors": [
    "Hao Xing"
  ],
  "comment": "Keywords: Backward stochastic differential equation, strict local martingale, viscosity solution, comparison theorem",
  "categories": [
    "math.PR"
  ],
  "abstract": "We study a backward stochastic differential equation whose terminal condition is an integrable function of a local martingale and generator has bounded growth in $z$. When the local martingale is a strict local martingale, the BSDE admits at least two different solutions. Other than a solution whose first component is of class D, there exists another solution whose first component is not of class D and strictly dominates the class D solution. Both solutions are $\\mathbb{L}^p$ integrable for any $0<p<1$. These two different BSDE solutions generate different viscosity solutions to the associated quasi-linear partial differential equation. On the contrary, when a Lyapunov function exists, the local martingale is a martingale and the quasi-linear equation admits a unique viscosity solution of at most linear growth.",
  "revisions": [
    {
      "version": "v4",
      "updated": "2011-12-12T09:43:41.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "backward stochastic differential equation",
      "strict local martingale",
      "first component",
      "viscosity solution",
      "associated quasi-linear partial differential equation"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2011arXiv1105.2973X"
    }
  }
}