  This paper investigates the dependence of functional portfolio generation,
introduced by Fernholz (1999), on an extra finite variation process. The
framework of Karatzas and Ruf (2017) is used to formulate conditions on trading
strategies to be strong arbitrage relative to the market over sufficiently
large time horizons. A mollification argument and Komlos theorem yield a
general class of potential arbitrage strategies. These theoretical results are
complemented by several empirical examples using data from the S&P 500 stocks.
