{
  "id": "2308.14506",
  "version": "v1",
  "published": "2023-08-28T11:46:56.000Z",
  "updated": "2023-08-28T11:46:56.000Z",
  "title": "Stochastic optimal control problems with delays in the state and in the control via viscosity solutions and an economical application",
  "authors": [
    "Filippo de Feo"
  ],
  "comment": "arXiv admin note: substantial text overlap with arXiv:2302.08809",
  "categories": [
    "math.OC",
    "math.AP",
    "math.PR"
  ],
  "abstract": "In this manuscript we consider optimal control problems of deterministic and stochastic differential equations with delays in the state and in the control. First we prove an equivalent Markovian reformulation on Hilbert spaces of the state equation. Then, using the dynamic programming approach for infinite-dimensional systems, we prove that the value function is the unique viscosity solution of the infinite-dimensional Hamilton Jacobi Bellman equation. Finally we apply this result to a stochastic optimal advertising problem with delays in the state and in the control.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-08-28T11:46:56.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "stochastic optimal control problems",
      "viscosity solution",
      "economical application",
      "infinite-dimensional hamilton jacobi bellman equation"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}