Monotone Mean-Variance Portfolio Selection in Semimartingale Markets: Martingale Method

2024/03/10 by Li, Yuchen, Liang, Zongxia, Pang, Shunzhi
#91B16 #91G10 #93E20 #FOS: Mathematics #Optimization and Control (math.OC)

paper · doi:10.48550/arxiv.2403.06190

Abstract

We use the martingale method to discuss the relationship between mean-variance (MV) and monotone mean-variance (MMV) portfolio selections. We propose a unified framework to discuss the relationship in general financial markets without any specific setting or completeness requirement. We apply this framework to a semimartingale market and find that MV and MMV are consistent if and only if the variance-optimal signed martingale measure keeps non-negative. Further, we provide an example to show the application of our result.

Related

• Strictly monotone mean-variance preferences with applications to portfolio selection
• Continuous-Time Monotone Mean-Variance Portfolio Selection in Jump-Diffusion Model
• Dynamically optimal portfolios for monotone mean--variance preferences
• Comparison Between Mean-Variance and Monotone Mean-Variance Preferences Under Jump Diffusion and Stochastic Factor Model
• Constrained monotone mean-variance problem with random coefficients