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Almost twenty years ago, E.R. Fernholz introduced portfolio generatingfunctions which can be used to construct a variety of portfolios, solely in theterms of the individual companies' market weights. I. Karatzas and J. Rufrecently developed another methodology for the functional construction ofportfolios, which leads to very simple conditions for strong relative arbitragewith respect to the market. In this paper, both of these notions of functionalportfolio generation are generalized in a pathwise, probability-free setting;portfolio generating functions are substituted by path-dependent functionals,which involve the current market weights, as well as additionalbounded-variation functions of past and present market weights. Thisgeneralization leads to a wider class of functionally-generated portfolios thanwas heretofore possible, and yields improved conditions for outperforming themarket portfolio over suitable time-horizons.

Trading Strategies Generated Pathwise by Functions of Market Weights