{
  "id": "2110.13056",
  "version": "v2",
  "published": "2021-10-25T15:51:10.000Z",
  "updated": "2023-12-04T19:08:50.000Z",
  "title": "Optimal stopping of an Ornstein-Uhlenbeck bridge",
  "authors": [
    "Abel Azze",
    "Bernardo D'Auria",
    "Eduardo García-Portugués"
  ],
  "comment": "22 pages, 3 figures",
  "categories": [
    "math.PR"
  ],
  "abstract": "We make a rigorous analysis of the existence and characterization of the free boundary related to the optimal stopping problem that maximizes the mean of an Ornstein--Uhlenbeck bridge. The result includes the Brownian bridge problem as a limit case. The methodology hereby presented relies on a time-space transformation that casts the original problem into a more tractable one with an infinite horizon and a Brownian motion underneath. We comment on two different numerical algorithms to compute the free-boundary equation and discuss illustrative cases that shed light on the boundary's shape. In particular, the free boundary generally does not share the monotonicity of the Brownian bridge case.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2023-12-04T19:08:50.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60G40",
      "60J60"
    ],
    "keywords": [
      "ornstein-uhlenbeck bridge",
      "optimal stopping",
      "free boundary",
      "brownian bridge case",
      "brownian motion underneath"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 22,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}