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

TL;DR

This paper extends capital growth theory to markets with transaction costs using the von Neumann-Gale model, introducing generalized numeraire portfolios for growth optimization.

Contribution

It proposes a new generalization of the numeraire portfolio concept within a stochastic von Neumann-Gale framework, addressing market frictions.

Findings

Defined a generalized numeraire portfolio for markets with transaction costs.

Showed how these portfolios can optimize growth in such markets.

Provided a stochastic model for financial markets with frictions.

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.