{
  "id": "2306.14615",
  "version": "v1",
  "published": "2023-06-26T11:40:34.000Z",
  "updated": "2023-06-26T11:40:34.000Z",
  "title": "Reflections on BSDEs",
  "authors": [
    "Dylan Possamaï",
    "Marco Rodrigues"
  ],
  "categories": [
    "math.PR",
    "math.OC"
  ],
  "abstract": "We consider backward stochastic differential equations (BSDEs) and reflected BSDEs in the generality that should in principle allow for a unified study of certain discrete-time and continuous-time control problems. We provide well-posedness results for the BSDEs and reflected BSDEs with optional obstacle process in case of appropriately weighted $\\mathbb{L}^2$-data. We compare our well-posedness results with the current literature and point out that our well-posedness result for the BSDE is sharp within the framework presented here. Finally, we provide sufficient conditions for a comparison principle.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-06-26T11:40:34.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "well-posedness result",
      "reflections",
      "backward stochastic differential equations",
      "optional obstacle process",
      "continuous-time control problems"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}