{
  "id": "1207.5491",
  "version": "v1",
  "published": "2012-07-23T19:14:40.000Z",
  "updated": "2012-07-23T19:14:40.000Z",
  "title": "On the Optimal Stopping of a One-dimensional Diffusion",
  "authors": [
    "Damien Lamberton",
    "Mihail Zervos"
  ],
  "journal": "Electronic Journal of Probability 18, 34 (2013) 1-49",
  "doi": "10.1214/EJP.v18-2182",
  "categories": [
    "math.PR"
  ],
  "abstract": "We consider a one-dimensional diffusion which solves a stochastic differential equation with Borel-measurable coefficients in an open interval. We allow for the endpoints to be inaccessible or absorbing. Given a Borel-measurable function $r$ that is uniformly bounded away from 0, we establish a new analytic representation of the $r$-potential of a continuous additive functional of the diffusion. We also characterize the value function of an optimal stopping problem with general reward function as the unique solution of a variational inequality (in the sense of distributions) with appropriate growth or boundary conditions. Furthermore, we establish several other characterisations of the solution to the optimal stopping problem, including a generalisation of the so-called \"principle of smooth fit\".",
  "revisions": [
    {
      "version": "v1",
      "updated": "2012-07-23T19:14:40.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "one-dimensional diffusion",
      "optimal stopping problem",
      "stochastic differential equation",
      "general reward function",
      "analytic representation"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2012arXiv1207.5491L"
    }
  }
}