{
  "id": "1106.1400",
  "version": "v4",
  "published": "2011-06-07T17:51:28.000Z",
  "updated": "2013-12-13T12:14:01.000Z",
  "title": "Minimal supersolutions of convex BSDEs",
  "authors": [
    "Samuel Drapeau",
    "Gregor Heyne",
    "Michael Kupper"
  ],
  "comment": "Published in at http://dx.doi.org/10.1214/13-AOP834 the Annals of Probability (http://www.imstat.org/aop/) by the Institute of Mathematical Statistics (http://www.imstat.org)",
  "journal": "Annals of Probability 2013, Vol. 41, No. 6, 3973-4001",
  "doi": "10.1214/13-AOP834",
  "categories": [
    "math.PR"
  ],
  "abstract": "We study the nonlinear operator of mapping the terminal value $\\xi$ to the corresponding minimal supersolution of a backward stochastic differential equation with the generator being monotone in $y$, convex in $z$, jointly lower semicontinuous and bounded below by an affine function of the control variable $z$. We show existence, uniqueness, monotone convergence, Fatou's lemma and lower semicontinuity of this operator. We provide a comparison principle for minimal supersolutions of BSDEs.",
  "revisions": [
    {
      "version": "v4",
      "updated": "2013-12-13T12:14:01.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "convex bsdes",
      "backward stochastic differential equation",
      "corresponding minimal supersolution",
      "terminal value",
      "nonlinear operator"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2011arXiv1106.1400D"
    }
  }
}