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 modelling of financial markets with frictions.
Disclosure statement
No potential conflict of interest was reported by the authors.
Notes
1 Chapter 9 of the monograph [Citation21] presents the main results of the papers [Citation19,Citation20].
2 A set in a linear space is called a (convex) cone if it contains together with any vectors a and b the vector , where λ and μ are any non-negative numbers. We will assume that all the cones under consideration contain non-zero vectors.
3 A set is said to depend
-measurably on ω if the graph
of the multivalued mapping
belongs to the σ-algebra
, where
is the Borel σ-algebra. A random set is a set
depending
-measurably on ω.
4 Models of currency markets with proportional transaction costs (bid-ask spreads) were developed by Kabanov and co-authors – see, e.g. [Citation38,Citation41] and references therein.