{
  "id": "1706.09651",
  "version": "v1",
  "published": "2017-06-29T09:41:02.000Z",
  "updated": "2017-06-29T09:41:02.000Z",
  "title": "Forward Backward Stochastic Differential Equation Games with Delay and Noisy Memory",
  "authors": [
    "Kristina Rognlien Dahl"
  ],
  "comment": "19 pages",
  "categories": [
    "math.OC"
  ],
  "abstract": "The main goal of this paper is to study a stochastic game connected to a system of forward backward stochastic differential equations (FBSDEs) involving delay and so-called noisy memory. We derive suffcient and necessary maximum principles for a set of controls for the players to be a Nash equilibrium in such a game. Furthermore, we study a corresponding FBSDE involving Malliavin derivatives, which (to the best of our knowledge) is a kind of equation which has not been studied before. The maximum principles give conditions for determining the Nash equilibrium of the game. We use this to derive a closed form Nash equilibrium for a specifc model in economics where the players aim to maximize their consumption with respect recursive utility.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-06-29T09:41:02.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "91A05",
      "91A15",
      "60H20",
      "60H10",
      "60J75",
      "34K50"
    ],
    "keywords": [
      "forward backward stochastic differential equation",
      "backward stochastic differential equation games",
      "noisy memory",
      "nash equilibrium",
      "maximum principles"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 19,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}