We pursue robust approach to pricing and hedging options in quantitative finance. The super-hedging problem is to construct a minimal hedging portfolio that dominates the payoff of the option, and the hedging duality is a useful tool to express this super-hedging price. Hedging duality is closely related to the fundamental theorem of asset pricing in a large financial market. In this talk, we discuss recent developments in robust hedging duality with connection to large financial market theory.