TRAJECTORY-BASED MODELS, ARBITRAGE AND CONTINUITY

In a nonprobabilistic setting, we prove general trajectory-based models to have no free lunch with vanishing risk. The main ingredient is a local continuity requirement on the final portfolio value considered as a functional on the trajectory space. This is shown to be a natural assumption by establishing that a large class of practical trading strategies, defined by means of trajectory-based stopping times, give rise to locally continuous functionals. The theory is applied to two specific trajectory models of practical interest. The established results are then used to derive no free lunch results for nonsemimartingale stochastic models.