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

Claudio Fontana (1)

1 MATHRISK - Mathematical Risk handling

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.

On donne une analyse critique de la preuve du théorème fondamental d'évaluation d'actifs proposé dans le papier Arbitrage and approximate arbitrage: the fundamental theorem of asset pricing par B. Wong et C.C. Heyde (Stochastics, 2010) dans le cadre de modèles incomplets dirigés par des processus d'Itô. On démontre que la technique de Wong et Heyde n'est valide que dans le cas bien connu d'un marché complet et on exhibe un contre-exemple explicite.

Domaines: Pricing [q-fin.PR]; Probabilités [math.PR]; Economies et finances

Claudio Fontana. A note on arbitrage, approximate arbitrage and the fundamental theorem of asset pricing. [Research Report] RR-8292, INRIA. 2013. ⟨hal-00818487⟩