Many studies on Prospect Theory (PT) and Cumulative Prospect Theory (CPT) applied to traffic assignment are based on static implementations and on small networks. Up to today and to the best of the author's knowledge, there are only two studies that discuss an extension of CPT to account for the route travel time distributions [15,19]. And, the application of PT, considering route travel time distributions and a dynamic traffic simulator, has not yet been analyzed in detail. In this paper, we revisit the concept of prospect-based User Equilibrium and discuss a different framework to account for timedependent route travel times considering the PT. We then consider that users perceive the route travel time with uncertainty that is modeled using Monte Carlo simulations. We present our assignment model proposition as a nonlinear mathematical program and discuss a solution algorithm based on the Method of Successive Averages (MSA). We discuss a dynamic implementation of the model, using a LWR mesoscopic simulator [20], on a 6 x 10 Grid network. The equilibrium results are compared against the Deterministic User Equilibrium (DUE) and Stochastic User Equilibrium (SUE).