{
  "id": "2211.14473",
  "version": "v1",
  "published": "2022-11-26T04:13:15.000Z",
  "updated": "2022-11-26T04:13:15.000Z",
  "title": "Comparison Between Mean-Variance and Monotone Mean-Variance Preferences Under Jump Diffusion and Stochastic Factor Model",
  "authors": [
    "Yuchen Li",
    "Zongxia Liang",
    "Shunzhi Pang"
  ],
  "categories": [
    "math.OC"
  ],
  "abstract": "This paper considers optimal investment problems based on monotone mean-variance and mean-variance preferences in L\\'evy market with an untradable stochastic factor. We focus on the comparison of optimal strategies and value functions in two problems. It is an open question proposed by Trybula and Zawisza. Using dynamic programming and the Lagrange multiplier method, we get Hamilton-Jacobi-Bellman-Isaacs equations (HJBI) and Hamilton-Jacobi-Bellman equations (HJB) corresponding to the two investment problems. The equations are transformed into a new-type parabolic equation, from which the optimal strategies under both preferences are derived. We prove that optimal strategies and value functions coincide in two investment problems, which means that investors with mean-variance preference act as they have a monotone preference. This phenomenon is interesting as that contradicts the results in single-period investment problems, even under our discontinuous market model. In addition, we derive the efficient frontier and analyze the economic impact of jump diffusion part in the risky asset.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-11-26T04:13:15.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "monotone mean-variance preferences",
      "stochastic factor model",
      "jump diffusion",
      "optimal strategies",
      "comparison"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}