No-arbitrage of second kind in countable markets with proportional transaction costs

TL;DR

This paper develops a multivariate framework for discrete-time financial markets with infinitely many assets and proportional transaction costs, establishing key properties related to no-arbitrage conditions and consistent pricing.

Contribution

It extends the no-arbitrage of second kind concept to countable markets, linking it to closure properties and the existence of consistent price systems.

Findings

NA2 property ensures closure of attainable claims

Equivalence between NA2 and existence of consistent price systems

Framework applicable to bond markets with infinite assets

Abstract

Motivated by applications to bond markets, we propose a multivariate framework for discrete time financial markets with proportional transaction costs and a countable infinite number of tradable assets. We show that the no-arbitrage of second kind property (NA2 in short), recently introduced by Rasonyi for finite-dimensional markets, allows us to provide a closure property for the set of attainable claims in a very natural way, under a suitable efficient friction condition. We also extend to this context the equivalence between NA2 and the existence of many (strictly) consistent price systems.