{
  "id": "1210.0628",
  "version": "v1",
  "published": "2012-10-02T01:20:38.000Z",
  "updated": "2012-10-02T01:20:38.000Z",
  "title": "Reflected Mean-Field Backward Stochastic Differential Equations. Approximation and Associated Nonlinear PDEs",
  "authors": [
    "Juan Li"
  ],
  "comment": "The paper was submitted",
  "categories": [
    "math.PR",
    "math.AP"
  ],
  "abstract": "Mathematical mean-field approaches have been used in many fields, not only in Physics and Chemistry, but also recently in Finance, Economics, and Game Theory. In this paper we will study a new special mean-field problem in a purely probabilistic method, to characterize its limit which is the solution of mean-field backward stochastic differential equations (BSDEs) with reflections. On the other hand, we will prove that this type of reflected mean-field BSDEs can also be obtained as the limit equation of the mean-field BSDEs by penalization method. Finally, we give the probabilistic interpretation of the nonlinear and nonlocal partial differential equations with the obstacles by the solutions of reflected mean-field BSDEs.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2012-10-02T01:20:38.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60H10",
      "60B10"
    ],
    "keywords": [
      "mean-field backward stochastic differential equations",
      "reflected mean-field backward stochastic differential",
      "associated nonlinear pdes",
      "mean-field bsdes"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2012arXiv1210.0628L"
    }
  }
}