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

2009/09/25 by Bahsoun, Wael, Evstigneev, Igor V., Taksar, Michael I.
#37H15 #37H99 #91B28 #91B62 #FOS: Economics and business #FOS: Mathematics #Portfolio Management (q-fin.PM) #Probability (math.PR)

paper · doi:10.48550/arxiv.0909.4730

Abstract

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.

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