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

Abstract

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.

Keywords

• Model uncertainty
• bid-ask prices for options
• semi-static hedging
• non-dominated collection of probability measures
• Fundamental Theorem of Asset Pricing
• super-hedging
• robust no-arbitrage
• non-redundant options