Mean-variance portfolio selection in jump-diffusion model under no-shorting constraint: A viscosity solution approach

ArXiv ID: 2406.03709 “View on arXiv”

Authors: Unknown

Abstract

This paper concerns a continuous time mean-variance (MV) portfolio selection problem in a jump-diffusion financial model with no-shorting trading constraint. The problem is reduced to two subproblems: solving a stochastic linear-quadratic (LQ) control problem under control constraint, and finding a maximal point of a real function. Based on a two-dimensional fully coupled ordinary differential equation (ODE), we construct an explicit viscosity solution to the Hamilton-Jacobi-Bellman equation of the constrained LQ problem. Together with the Meyer-Itô formula and a verification procedure, we obtain the optimal feedback controls of the constrained LQ problem and the original MV problem, which corrects the flawed results in some existing literatures. In addition, closed-form efficient portfolio and efficient frontier are derived. In the end, we present several examples where the two-dimensional ODE is decoupled.

Keywords: Mean-Variance Portfolio Selection, Jump-Diffusion, Hamilton-Jacobi-Bellman Equation, Viscosity Solution, No-Shorting Constraint, Equities / Portfolio Management

Complexity vs Empirical Score

  • Math Complexity: 9.5/10
  • Empirical Rigor: 2.0/10
  • Quadrant: Lab Rats
  • Why: The paper is highly theoretical, employing advanced stochastic control, viscosity solutions, and fully coupled ODEs with rigorous proofs, but lacks any empirical backtesting, code, or real data analysis, focusing solely on mathematical derivation.
  flowchart TD
    A["Research Goal: Optimal MV Portfolio in Jump-Diffusion Model with No-Shorting Constraint"] --> B["Formulate Stochastic LQ Control Problem"]
    B --> C["Derive HJB Equation & Constraints"]
    C --> D["Construct Viscosity Solution via 2D ODE"]
    D --> E["Apply Meyer-Itô Formula & Verification"]
    E --> F["Obtain Optimal Feedback Controls & Efficient Frontier"]
    F --> G["Outcome: Corrected Results & Closed-Form Solutions"]