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

Claudio Fontana
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Claudio Fontana: MATHRISK - Mathematical Risk handling - Inria Paris-Rocquencourt - Inria - Institut National de Recherche en Informatique et en Automatique - UPEM - Université Paris-Est Marne-la-Vallée - ENPC - École nationale des ponts et chaussées

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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, 2010) 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 and give an explicit counterexample.

Date: 2013-04-26
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Published in [Research Report] RR-8292, INRIA. 2013

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