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We provide a critical analysis of the proof of the fundamental theorem ofasset pricing given in the paper "Arbitrage and approximate arbitrage: thefundamental theorem of asset pricing" by B. Wong and C.C. Heyde (Stochastics,2010) in the context of incomplete It\^o-process models. We show that theirapproach can only work in the known case of a complete financial market modeland give an explicit counterexample.

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