Arbitrage and Hedging in model-independent markets with frictions

TL;DR

This paper establishes fundamental theorems linking no arbitrage, superhedging, and consistent price systems in a model-independent discrete-time market with transaction costs, extending classical results to frictional settings.

Contribution

It proves a Fundamental Theorem of Asset Pricing and a Superhedging Theorem under model-independent assumptions with transaction costs, introducing a probability-free no arbitrage condition.

Findings

Equivalence between robust no arbitrage and consistent price systems.

Superhedging price matches frictionless superhedging for a related process.

Extension of classical theorems to markets with proportional transaction costs.

Abstract

We provide a Fundamental Theorem of Asset Pricing and a Superhedging Theorem for a model independent discrete time financial market with proportional transaction costs. We consider a probability-free version of the Robust No Arbitrage condition introduced in Schachermayer ['04] and show that this is equivalent to the existence of Consistent Price Systems. Moreover, we prove that the superhedging price for a claim g coincides with the frictionless superhedging price of g for a suitable process in the bid-ask spread.