{
  "id": "1105.1471",
  "version": "v1",
  "published": "2011-05-07T19:43:57.000Z",
  "updated": "2011-05-07T19:43:57.000Z",
  "title": "Existence, minimality and approximation of solutions to BSDEs with convex drivers",
  "authors": [
    "Patrick Cheridito",
    "Mitja Stadje"
  ],
  "categories": [
    "math.PR"
  ],
  "abstract": "We study the existence of solutions to backward stochastic differential equations with drivers f(t,W,y,z) that are convex in z. We assume f to be Lipschitz in y and W but do not make growth assumptions with respect to z. We first show the existence of a unique solution (Y,Z) with bounded Z if the terminal condition is Lipschitz in W and that it can be approximated by the solutions to properly discretized equations. If the terminal condition is bounded and uniformly continuous in W, we show the existence of a minimal continuous supersolution by uniformly approximating the terminal condition with Lipschitz terminal conditions. Finally, we prove existence of a minimal RCLL supersolution for bounded lower semicontinuous terminal conditions by approximating the terminal condition pointwise from below with Lipschitz terminal conditions.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2011-05-07T19:43:57.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60H10",
      "65C30"
    ],
    "keywords": [
      "convex drivers",
      "lipschitz terminal conditions",
      "approximation",
      "minimality",
      "minimal rcll supersolution"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2011arXiv1105.1471C"
    }
  }
}