A note on arbitrage, approximate arbitrage and the fundamental theorem of asset pricing

Abstract

We provide a critical analysis of the proof of the fundamental theorem of asset pricing given in the paper Arbitrage and approximate arbitrage: the fundamental theorem of asset pricing by B. Wong and C.C. Heyde [Stochastics 82 (2010), pp. 189–200] in the context of incomplete Itô-process models. We show that their approach can only work in the known case of a complete financial market model and give an explicit counter example.