Before revision:  Here we generalize the class of FGPs in several ways: (1) they may be specified over any strictly positive wealth processes resulting from investment in the tradeable assets, (2) the num\'eraire may be any strictly positive wealth process, (3 ) generating functions may be stochastically dynamic, adjusting to changing market conditions through an auxiliary continuous-path stochastic argument of finite variation.
After revision:  Here we generalize the class of FGPs in several ways: (1) the num\'eraire may be any strictly positive wealth process, (3 ) generating functions may be stochastically dynamic, adjusting to changing market conditions through an auxiliary continuous-path stochastic argument of finite variation.