{
  "id": "2111.10597",
  "version": "v2",
  "published": "2021-11-20T14:14:26.000Z",
  "updated": "2022-12-16T17:09:15.000Z",
  "title": "A new monotonicity condition for ergodic BSDEs and ergodic control with super-quadratic Hamiltonians",
  "authors": [
    "Joe Jackson",
    "Gechun Liang"
  ],
  "categories": [
    "math.PR",
    "math.OC"
  ],
  "abstract": "We establish the existence (and in an appropriate sense uniqueness) of Markovian solutions for ergodic BSDEs under a novel monotonicity condition. Our monotonicity condition allows us to prove existence even when the driver f has arbitrary (in particular super-quadratic) growth in z, which reveals an interesting trade-off between monotonicity and growth for ergodic BSDEs. The technique of proof is to establish a probabilistic representation of the derivative of the Markovian solution, and then use this representation to obtain a-priori estimates. Our study is motivated by applications to ergodic control, and we use our existence result to prove the existence of optimal controls for a class of ergodic control problems with potentially super-quadratic Hamiltonians. We also treat a class of drivers coming from the construction of forward performance processes, and interpret our monotonicity condition in this setting.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2022-12-16T17:09:15.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60H30"
    ],
    "keywords": [
      "ergodic bsdes",
      "super-quadratic hamiltonians",
      "markovian solution",
      "novel monotonicity condition",
      "ergodic control problems"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}