Two Stochastic Control Methods for Mean-Variance Portfolio Selection of Jump Diffusions and Their Relationship

ArXiv ID: 2508.01138 “View on arXiv”

Authors: Qiyue Zhang, Jingtao Shi

Abstract

This paper is concerned with the maximum principle and dynamic programming principle for mean-variance portfolio selection of jump diffusions and their relationship. First, the optimal portfolio and efficient frontier of the problem are obtained using both methods. Furthermore, the relationship between these two methods is investigated. Specially, the connections between the adjoint processes and value function are given.

Keywords: Mean-Variance Optimization, Jump Diffusions, Maximum Principle, Dynamic Programming, Stochastic Control, 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, featuring dense stochastic control methods (maximum principle, dynamic programming, jump diffusions) with extensive formal derivations and ODE solutions, but it lacks any empirical backtesting, dataset usage, or implementation details.

  flowchart TD
    A["Research Goal<br>Mean-Variance Portfolio<br>Selection for Jump Diffusions"] --> B["Model Formulation<br>Stochastic Control Setup"]
    B --> C["Method 1: Maximum Principle<br>Adjoint Process & Hamiltonian"]
    B --> D["Method 2: Dynamic Programming<br>Hamilton-Jacobi-Bellman PDE"]
    C --> E["Computational Process<br>Optimal Portfolio Strategy"]
    D --> E
    E --> F["Key Outcomes<br>Efficient Frontier &<br>Link between Adjoint Process & Value Function"]