The Fatou Property under Model Uncertainty and the Fundamental Theorem of Asset Pricing

We provide a characterization in terms of Fatou property for weakly closed monotone sets in the space of P-quasisure bounded random variables, where P is a (eventually non-dominated) class of probability measures. Our results can be applied to obtain a topological deduction of the First Fundamental Theorem of Asset Pricing for discrete time processes, the dual representation of the superhedging price and more in general the robust dual representation for (quasi)convex increasing functionals.
This is a joint paper with T. Meyer-Brandis and G. Svindland.