{
  "id": "2410.04615",
  "version": "v1",
  "published": "2024-10-06T20:30:41.000Z",
  "updated": "2024-10-06T20:30:41.000Z",
  "title": "Time-reversal solution of BSDEs in stochastic optimal control: a linear quadratic study",
  "authors": [
    "Yuhang Mei",
    "Amirhossein Taghvaei"
  ],
  "comment": "7 pages, 4 figures, 1 table",
  "categories": [
    "math.OC"
  ],
  "abstract": "This paper addresses the numerical solution of backward stochastic differential equations (BSDEs) arising in stochastic optimal control. Specifically, we investigate two BSDEs: one derived from the Hamilton-Jacobi-Bellman equation and the other from the stochastic maximum principle. For both formulations, we analyze and compare two numerical methods. The first utilizes the least-squares Monte-Carlo (LSMC) approach for approximating conditional expectations, while the second leverages a time-reversal (TR) of diffusion processes. Although both methods extend to nonlinear settings, our focus is on the linear-quadratic case, where analytical solutions provide a benchmark. Numerical results demonstrate the superior accuracy and efficiency of the TR approach across both BSDE representations, highlighting its potential for broader applications in stochastic control.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-10-06T20:30:41.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "stochastic optimal control",
      "linear quadratic study",
      "time-reversal solution",
      "backward stochastic differential equations",
      "stochastic maximum principle"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 7,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}