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) 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, not necessarily the market portfolio or even a passive portfolio; (2 ) generating functions may be stochastically dynamic, adjusting to changing market conditions through an auxiliary continuous-path stochastic argument of finite variation.