Comparison Between Mean-Variance and Monotone Mean-Variance Preferences Under Jump Diffusion and Stochastic Factor Model

• 成果类型: Article
• 署名作者: Li, Yuchen; Liang, Zongxia; Pang, Shunzhi
• 署名单位: Tsinghua University; Tsinghua University
• 刊物名称: MATHEMATICS OF OPERATIONS RESEARCH
• ISSN/ISSBN: 0364-765X
• DOI: 10.1287/moor.2022.0331
• 发表日期: 2025
• 关键词: portfolio selection; random parameters

摘要

This paper compares the optimal investment problems based on monotone mean-variance (MMV) and mean-variance (MV) preferences in a Levy market with an untradable stochastic factor. It is an open question proposed by Trybu & lstrok;a and Zawisza. Using the dynamic programming and Lagrange multiplier methods, we get the HamiltonJacobi-Bellman-Isaacs (HJBI) and Hamilton-Jacobi-Bellman (HJB) equations 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 the two optimal strategies and value functions coincide if and only if an important market assumption holds. When the assumption is violated, MMV investors act differently from MV investors. Thus, we conclude that the difference between continuous-time MMV and MV portfolio selections is due to the discontinuity of the market. In addition, we derive the efficient frontier and analyze the economic impact of the jump diffusion risky asset. We also provide empirical evidence to demonstrate the validity of the assumption in real financial markets.