Von Neumann-Gale Model, Market Frictions, and Capital Growth

Abstract

The aim of this work is to extend the classical capital growth theory pertaining to frictionless financial markets to models taking into account various kinds of frictions, including transaction costs and portfolio constraints. A natural generalization of the notion of a benchmark investment strategy (Platen, Heath and others) is proposed, and it is shown how such strategies can be used for the analysis of growth-optimal investments. The analysis is based on the classical von Neumann-Gale model of economic growth, a stochastic version of which is used in this study as a framework for the modeling of financial markets with frictions.

Keywords: capital growth theory, transaction costs, benchmark strategies, numeraire portfolios, random dynamical systems, convex multivalued operators, von Neumann-Gale dynamical systems, rapid paths

JEL Classification: C61, C62, O41, G10