Title: Trading Strategies Generated by Path-dependent Functionals of Market Weights,
Abstract: Almost twenty years ago, E.R. Fernholz introduced portfolio generating
functions which can be used to construct a variety of portfolios, solely in the
terms of the individual companies' market weights. I. Karatzas and J. Ruf
recently developed another methodology for the functional construction of
portfolios, which leads to very simple conditions for strong relative arbitrage
with respect to the market. In this paper, both of these notions of functional
portfolio 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 additional
bounded-variation functions of past and present market weights. This
generalization leads to a wider class of functionally-generated portfolios than
was heretofore possible, and yields improved conditions for outperforming the
market portfolio over suitable time-horizons.