A Note on the Fundamental Theorem of Asset Pricing under Model Uncertainty

We show that the recent results on the Fundamental Theorem of Asset Pricing and the super-hedging theorem in the context of model uncertainty can be extended to the case in which the options available for static hedging (hedging options) are quoted with bid-ask spreads. In this set-up, we need to wo...

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Bibliographic Details
Main Authors: Erhan Bayraktar, Yuchong Zhang, Zhou Zhou
Format: Article
Language:English
Published: MDPI AG 2014-10-01
Series:Risks
Subjects:
Online Access:http://www.mdpi.com/2227-9091/2/4/425
Description
Summary:We show that the recent results on the Fundamental Theorem of Asset Pricing and the super-hedging theorem in the context of model uncertainty can be extended to the case in which the options available for static hedging (hedging options) are quoted with bid-ask spreads. In this set-up, we need to work with the notion of robust no-arbitrage which turns out to be equivalent to no-arbitrage under the additional assumption that hedging options with non-zero spread are non-redundant. A key result is the closedness of the set of attainable claims, which requires a new proof in our setting.
ISSN:2227-9091