{
  "id": "1105.0881",
  "version": "v1",
  "published": "2011-05-04T17:56:12.000Z",
  "updated": "2011-05-04T17:56:12.000Z",
  "title": "A New Class of Backward Stochastic Partial Differential Equations with Jumps and Applications",
  "authors": [
    "Wanyang Dai"
  ],
  "comment": "22 pagea, 1 figure",
  "categories": [
    "math.PR",
    "cs.SY",
    "math-ph",
    "math.AP",
    "math.MP",
    "math.OC",
    "math.ST",
    "stat.TH"
  ],
  "abstract": "We formulate a new class of stochastic partial differential equations (SPDEs), named high-order vector backward SPDEs (B-SPDEs) with jumps, which allow the high-order integral-partial differential operators into both drift and diffusion coefficients. Under certain type of Lipschitz and linear growth conditions, we develop a method to prove the existence and uniqueness of adapted solution to these B-SPDEs with jumps. Comparing with the existing discussions on conventional backward stochastic (ordinary) differential equations (BSDEs), we need to handle the differentiability of adapted triplet solution to the B-SPDEs with jumps, which is a subtle part in justifying our main results due to the inconsistency of differential orders on two sides of the B-SPDEs and the partial differential operator appeared in the diffusion coefficient. In addition, we also address the issue about the B-SPDEs under certain Markovian random environment and employ a B-SPDE with strongly nonlinear partial differential operator in the drift coefficient to illustrate the usage of our main results in finance.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2011-05-04T17:56:12.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "backward stochastic partial differential equations",
      "nonlinear partial differential operator",
      "high-order vector backward spdes",
      "applications"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 22,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2011arXiv1105.0881D"
    }
  }
}