The fundamental theorem of asset pricing with and without transaction costs

TL;DR

This paper establishes a version of the fundamental theorem of asset pricing in continuous time that applies to both markets with and without transaction costs, using a strict no-arbitrage condition.

Contribution

It extends the FTAP to markets with proportional transaction costs without requiring the usual boundedness or concatenation properties.

Findings

Validates FTAP under strict no-arbitrage in continuous markets

Applicable to markets with bid-ask spreads and frictionless markets

Does not require bounded trading volume or concatenation property

Abstract

We prove a version of the fundamental theorem of asset pricing (FTAP) in continuous time that is based on the strict no-arbitrage condition and that is applicable to both frictionless markets and markets with proportional transaction costs. We consider a market with a single risky asset whose ask price process is higher than or equal to its bid price process. Neither the concatenation property of the set of wealth processes, that is used in the proof of the frictionless FTAP, nor some boundedness property of the trading volume of admissible strategies usually argued with in models with a nonvanishing bid-ask spread need to be satisfied in our model.