A note on the fundamental theorem of asset pricing under model uncertainty - Erhan Bayraktar; Yuchong Zhang; Zhou Zhou (Risks, 2014)
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: 330; 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