A model-free version of the Fundamental Theorem of Asset Pricing and the Super-Replication Theorem

We propose a Fundamental Theorem of Asset Pricing and a Super-Replication Theorem in a modelindependent framework. We prove these theorems in the setting of finite, discrete time and a market consisting of a risky asset S as well as options written on this risky asset. As a technical condition, we assume the existence of a traded option with a super-linearly growing payo-function, e.g., a power option. This condition is not needed when suciently many vanilla options maturing at the horizon T are traded in the market.