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

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.Comment: Final version. To appear in Risk

Comparison of viscosity solutions for a class of second order PDEs on the Wasserstein space

We prove a comparison result for viscosity solutions of second order parabolic partial differential equations in the Wasserstein space. The comparison is valid for semisolutions that are Lipschitz continuous in the measure in a Fourier-Wasserstein metric and uniformly continuous in time. The class of equations we consider is motivated by Mckean-Vlasov control problems with common noise and filtering problems. The proof of comparison relies on a novel version of Ishii's lemma, which is tailor-made for the class of equations we consider.Comment: Keywords: Wasserstein space, second order PDEs, viscosity solutions, comparison principle, Ishii's Lemma. In version 2 some small typos are fixe