Continuous-Time Monotone Mean-Variance Portfolio Selection

We study the continuous-time portfolio selection under monotone mean-variance (MMV) preferences in a jump-diffusion model and give an explicit solution different from that under classical mean-variance (MV) preferences for the first time. We prove that ambiguity measures of MMV can be restricted on non-negative Dol\'eans-Dade exponentials. We find that MMV can fix the non-monotonicity of MV when the jump size of the financial market can be larger than the inverse of the market price of risk. Such result is completely comparable to the earliest result of Dybvig and Ingersoll. Further, we verify the validity of two-fund separation and establish the monotone capital asset pricing model (monotone CAPM) for MMV investors. We also study MMV in a constrained trading model and provide three specific numerical examples to show MMV's efficiency. Our finding can be an important theoretical basis for future empirical tests of MMV and monotone CAPM's effectiveness.