{
  "id": "math/0602453",
  "version": "v1",
  "published": "2006-02-21T10:40:21.000Z",
  "updated": "2006-02-21T10:40:21.000Z",
  "title": "Small time path behavior of double stochastic integrals and applications to stochastic control",
  "authors": [
    "Patrick Cheridito",
    "H. Mete Soner",
    "Nizar Touzi"
  ],
  "comment": "Published at http://dx.doi.org/10.1214/105051605000000557 in the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org)",
  "journal": "Annals of Applied Probability 2005, Vol. 15, No. 4, 2472-2495",
  "doi": "10.1214/105051605000000557",
  "categories": [
    "math.PR"
  ],
  "abstract": "We study the small time path behavior of double stochastic integrals of the form $\\int_0^t(\\int_0^rb(u) dW(u))^T dW(r)$, where $W$ is a $d$-dimensional Brownian motion and $b$ is an integrable progressively measurable stochastic process taking values in the set of $d\\times d$-matrices. We prove a law of the iterated logarithm that holds for all bounded progressively measurable $b$ and give additional results under continuity assumptions on $b$. As an application, we discuss a stochastic control problem that arises in the study of the super-replication of a contingent claim under gamma constraints.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2006-02-21T10:40:21.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60G17",
      "60H05",
      "60H30",
      "91B28"
    ],
    "keywords": [
      "small time path behavior",
      "double stochastic integrals",
      "stochastic control",
      "progressively measurable stochastic process",
      "application"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2006math......2453C"
    }
  }
}