Continuous-Time Monotone Mean-Variance Portfolio Selection in Jump-Diffusion Model

Abstract: We study continuous-time portfolio selection under monotone mean-variance (MMV) preferences in a jump-diffusion model, presenting an explicit solution different from that under classical mean-variance (MV) preferences in dynamic settings for the first time. We prove that the potential measures calculating MMV preferences can be restricted to non-negative Dol\'eans-Dade exponentials. We find that MMV can resolve the non-monotonicity and free cash flow stream problems of MV when the jump size can be larger than the inverse of the market price of risk. Such result is completely comparable to the earliest result by Dybvig and Ingersoll. Economically, we show that the essence of MMV lies in the pricing operator always remaining non-negative, with a value of zero assigned when the jump exceeds a certain threshold, avoiding the issue of non-monotonicity. As a result, MMV investors behave markedly different from MV investors. Furthermore, we validate the 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 serve as a crucial theoretical foundation for future empirical tests of MMV and monotone CAPM's effectiveness.