  We consider the fundamental theorem of asset pricing (FTAP) and hedging
prices of options under non-dominated model uncertainty and portfolio
constrains in discrete time. We first show that no arbitrage holds if and only
if there exists some family of probability measures such that any admissible
portfolio value process is a local super-martingale under these measures. We
also get the non-dominated optional decomposition with constraints. From this
decomposition, we get duality of the super-hedging prices of European options,
as well as the sub- and super-hedging prices of American options. Finally, we
get the FTAP and duality of super-hedging prices in a market where stocks are
traded dynamically and options are traded statically.

Probability;Optimization and Control;General Finance