{
  "id": "1009.1042",
  "version": "v1",
  "published": "2010-09-06T12:45:21.000Z",
  "updated": "2010-09-06T12:45:21.000Z",
  "title": "Backward stochastic differential equations under super linear G-expectation and associated Hamilton-Jacobi-Bellman equations",
  "authors": [
    "Yuhong Xu"
  ],
  "comment": "21 pages",
  "categories": [
    "math.PR",
    "math.OC"
  ],
  "abstract": "This paper first studies super linear G-expectation. Uniqueness and existence theorem for backward stochastic differential equations (BSDEs) under super linear expectation is established to provide probabilistic interpretation for the viscosity solution of a class of Hamilton-Jacobi-Bellman equations, including the well known Black-Scholes-Barrenblett equation, arising in the uncertainty volatility model in mathematical finance. We also show that BSDEs under super linear expectation could characterize a class of stochastic control problems. A direct connection between recursive super (sub) strategies with mutually singular probability measures and classical stochastic control problems is provided. By this result we give representation for solutions of Black-Scholes-Barrenblett equations and G-heat equations.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2010-09-06T12:45:21.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60H10",
      "60H30",
      "60J65",
      "35K55",
      "35K05",
      "49L25"
    ],
    "keywords": [
      "backward stochastic differential equations",
      "associated hamilton-jacobi-bellman equations",
      "first studies super linear",
      "studies super linear g-expectation",
      "stochastic control problems"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 21,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2010arXiv1009.1042X"
    }
  }
}