论文标题
在跳跃扩散和随机因子模型下的均值变化和单调均值变化偏好之间的比较
Comparison Between Mean-Variance and Monotone Mean-Variance Preferences Under Jump Diffusion and Stochastic Factor Model
论文作者
论文摘要
本文比较了基于单调均值变化（MMV）和均值变化（MV）偏好的最佳投资问题，并以无法交易的随机因素进行比较。这是Trybuła和Zawisza提出的一个公开问题。使用动态编程和Lagrange乘数方法，我们获得了与两个投资问题相对应的HJBI和HJB方程。方程将转换为新型抛物线方程，从该方程中得出了两个偏好下的最佳策略。我们证明，当且仅当一个重要的市场假设成立时，两种最佳策略和价值功能是重合的。当假设违反时，MMV投资者的行动与MV投资者的行为不同。因此，我们得出的结论是，连续时间MMV和MV投资组合选择之间的差异是由于市场的不连续性所致。此外，我们得出了有效的边界，并分析了跳扩散风险资产的经济影响。我们还提供了经验证据，以证明在实际金融市场中假设的有效性。
This paper compares the optimal investment problems based on monotone mean-variance (MMV) and mean-variance (MV) preferences in the Lévy market with an untradable stochastic factor. It is an open question proposed by Trybuła and Zawisza. Using the dynamic programming and Lagrange multiplier methods, we get the HJBI and 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 violates, 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 evidences to demonstrate the validity of the assumption in real financial market.
