  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.
