No free lunch for markets with multiple num\'eraires

TL;DR

This paper develops a theoretical framework for markets composed of multiple submarkets, each with its own assets and numéraire, addressing the existence of equivalent martingale measures and superreplication prices.

Contribution

It introduces a novel theoretical foundation for analyzing markets with multiple numéraires, extending classical results to this more complex setting.

Findings

Existence conditions for equivalent martingale measures in multi-numéraire markets

Superreplication prices accounting for submarket differences

Theoretical insights into market completeness and arbitrage

Abstract

We consider a global market constituted by several submarkets, each with its own assets and num\'eraire. We provide theoretical foundations for the existence of equivalent martingale measures and results on superreplication prices which allows to take into account difference of features between submarkets.