The aim of this work is to extend the capital growth theory developed by
Kelly, Breiman, Cover and others to asset market models with transaction costs.
We define a natural generalization of the notion of a numeraire portfolio
proposed by Long and show how such portfolios can be used for constructing
growth-optimal investment strategies. The analysis is based on the classical
von Neumann-Gale model of economic dynamics, a stochastic version of which we
use as a framework for the modelling of financial markets with frictions.