A note on the Fundamental Theorem of Asset Pricing under model uncertainty

Erhan Bayraktar; Yuchong Zhang; Zhou Zhou

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arXiv · 1309.2728

A note on the Fundamental Theorem of Asset Pricing under model uncertainty

Erhan Bayraktar·Yuchong Zhang·Zhou Zhou

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Abstract

We show that the results of ArXiv:1305.6008 on the Fundamental Theorem of Asset Pricing and the super-hedging theorem can be extended to the case in which the options available for static hedging (\emph{hedging options}) are quoted with bid-ask spreads. In this set-up, we need to work with the notion of \emph{robust no-arbitrage} which turns out to be equivalent to no-arbitrage under the additional assumption that hedging options with non-zero spread are \emph{non-redundant}. A key result is the closedness of the set of attainable claims, which requires a new proof in our setting.

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Erhan Bayraktar, Yuchong Zhang, Zhou Zhou. 2014-09-29. A note on the Fundamental Theorem of Asset Pricing under model uncertainty. https://arxiv.org/abs/1309.2728

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