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 (hedging options) are quoted with bid-ask spreads. It turns out that the dual elements have to be martingale measures that need to price thenon-redundant hedging options correctly  . A key result is the closedness of the set of attainable claims, which requires a new proof in our setting.
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 (hedging options) are quoted with bid-ask spreads. In this set-up, we need to work with the notion ofrobust no-arbitrage which turns out to be equivalent to no-arbitrage under the additional assumption that hedging options with non-zero spread arenon-redundant . A key result is the closedness of the set of attainable claims, which requires a new proof in our setting.
D
It turns out that the dual elements have to be martingale measures that need to price the
D
non-redundant
R
hedging options correctly
In this set-up, we need to work with the notion of
A
robust no-arbitrage
A
which turns out to be equivalent to no-arbitrage under the additional assumption that hedging options with non-zero spread are
A
non-redundant