{
  "id": "1302.0442",
  "version": "v4",
  "published": "2013-02-03T01:12:19.000Z",
  "updated": "2015-09-18T12:43:55.000Z",
  "title": "Robust utility maximization with a general penalty term",
  "authors": [
    "Wahid Faidi",
    "Anis Matoussi",
    "Mohamed Mnif"
  ],
  "comment": "31 pages",
  "categories": [
    "math.PR"
  ],
  "abstract": "In this paper, a robust stochastic control problem with general penalty term is studied in the dominated case. Two types of penalties are considered. The first one is of type f-divergence penalty treated in the general framework of a continuous filtration. The second one called consistent time penalty studied in the context of a Brownian filtration. Existence and uniqueness of the optimal model of the robust problem are proved. Moreover, the optimal model is equivalent to the reference probability measure. In the case of consistent time penalty, we characterize the dynamic value process of our stochastic control problem as the unique solution of a class of quadratic backward stochastic differential equation with unbounbed terminal condition.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2013-10-09T22:59:24.000Z",
      "abstract": "We study a robust utility maximization problem with non entropic penalty term. We consider two types of Penalties. The first one is the f-divergence penalty studied in the general framework of a continuous filtration. The second called consistent time penalty studied in the context of a Brownian filtration. These Penalties generalizes the relative entropy. We prove in the two cases that there exists a unique optimal probability measure solution of the robust problem, which is equivalent to the historical probability. In the case of a consistent time penalty, we characterize the dynamic value process of our stochastic control problem as the unique solution of a quadratic backward stochastic differential equation.",
      "journal": null,
      "doi": null
    },
    {
      "version": "v4",
      "updated": "2015-09-18T12:43:55.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60H10",
      "60H30"
    ],
    "keywords": [
      "robust utility maximization",
      "general penalty term",
      "consistent time penalty",
      "unique optimal probability measure solution",
      "quadratic backward stochastic differential equation"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 31,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1302.0442F"
    }
  }
}