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

Growth-optimal investments and numeraire portfolios under transaction costs: An analysis based on the von Neumann-Gale model