{
  "id": "1902.11178",
  "version": "v1",
  "published": "2019-02-28T15:57:51.000Z",
  "updated": "2019-02-28T15:57:51.000Z",
  "title": "Small-time solvability of a flow of forward-backward stochastic differential equations",
  "authors": [
    "Yushi Hamaguchi"
  ],
  "comment": "29 pages",
  "categories": [
    "math.PR"
  ],
  "abstract": "Motivated from time-inconsistent stochastic control problems, we introduce a new type of coupled forward-backward stochastic systems, namely, flows of forward-backward stochastic differential equations. They are systems consisting of a single forward SDE and a continuum of BSDEs, which are defined on different time-intervals and connected via an equilibrium condition. We formulate a notion of equilibrium solutions in a general framework and prove small-time well-posedness of the equations. We also consider discretized flows and show that their equilibrium solutions approximate the original one, together with an estimate of the convergence rate.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-02-28T15:57:51.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "forward-backward stochastic differential equations",
      "small-time solvability",
      "time-inconsistent stochastic control problems",
      "equilibrium solutions approximate",
      "small-time well-posedness"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 29,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}