{
  "id": "2208.02581",
  "version": "v1",
  "published": "2022-08-04T11:10:50.000Z",
  "updated": "2022-08-04T11:10:50.000Z",
  "title": "A mass transport approach to the optimization of adapted couplings of real valued random variables",
  "authors": [
    "Rémi Lassalle"
  ],
  "comment": "Document of work in progess",
  "categories": [
    "math.PR",
    "math.OC"
  ],
  "abstract": "In this work, we investigate an optimization problem over adapted couplings between pairs of real valued random variables, possibly describing random times. We relate those couplings to a specific class of causal transport plans between probabilities on the set of real numbers endowed with a filtration, for which their provide a specific representation, which is motivated by a precise characterization of the corresponding deterministic transport plans. From this, under mild hypothesis, the existence of a solution to the problem investigated here is obtained. Furthermore, several examples are provided, within this explicit framework.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-08-04T11:10:50.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "real valued random variables",
      "mass transport approach",
      "adapted couplings",
      "optimization",
      "corresponding deterministic transport plans"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}