{
  "id": "2404.02871",
  "version": "v1",
  "published": "2024-04-03T17:08:23.000Z",
  "updated": "2024-04-03T17:08:23.000Z",
  "title": "A mean-field model of optimal investment",
  "authors": [
    "Alessandro Calvia",
    "Salvatore Federico",
    "Giorgio Ferrari",
    "Fausto Gozzi"
  ],
  "categories": [
    "math.OC",
    "econ.TH"
  ],
  "abstract": "We establish the existence and uniqueness of the equilibrium for a stochastic mean-field game of optimal investment. The analysis covers both finite and infinite time horizons, and the mean-field interaction of the representative company with a mass of identical and indistinguishable firms is modeled through the time-dependent price at which the produced good is sold. At equilibrium, this price is given in terms of a nonlinear function of the expected (optimally controlled) production capacity of the representative company at each time. The proof of the existence and uniqueness of the mean-field equilibrium relies on a priori estimates and the study of nonlinear integral equations, but employs different techniques for the finite and infinite horizon cases. Additionally, we investigate the deterministic counterpart of the mean-field game under study.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-04-03T17:08:23.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35Q89",
      "47H10",
      "49N10",
      "49N80",
      "91A07",
      "91B38",
      "91B70"
    ],
    "keywords": [
      "optimal investment",
      "mean-field model",
      "stochastic mean-field game",
      "infinite time horizons",
      "infinite horizon cases"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}