On general financial markets with concave transactions costs

TL;DR

This paper investigates financial markets with concave transaction costs, typical for small investors, establishing conditions for arbitrage absence and introducing a new concept of asymptotic arbitrage.

Contribution

It introduces a novel notion of asymptotic arbitrage and provides sufficient conditions for arbitrage absence in markets with concave transaction costs.

Findings

Conditions for absence of arbitrage established

Introduction of asymptotic arbitrage concept

Application to small investor markets like currency and real estate

Abstract

In the paper we study markets with concave transaction costs which depend in a concave way on the volume of transaction. This is typical situation in the case of small investors, which commonly appears in currency and real estate markets. Sufficient conditions for absence of arbitrage are formulated. New notion of asymptotic arbitrage is introduced and used to study the above mentioned markets.