Before revision:  Moreover, in our setting, the portfolio-generating function may depend on the entire history of the asset trajectories and on an additional continuous trajectory of bounded variation .
After revision:  Moreover, in our setting, the portfolio-generating function may depend on the current states of the market portfolio and an additional path of finite variation. The second version is formulated within the functional pathwise It\^o calculus of Dupire (2009) and Cont \& Fourni\'e (2010) and allows for portfolio-generating functionals that may depend additionally on the entire path of the market portfolio .