A model-free version of the fundamental theorem of asset pricing and the super-replication theorem

Beatrice Acciaio, Mathias Beiglb\"ock, Friedrich Penkner and Walter Schachermayer

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Abstract: We propose a Fundamental Theorem of Asset Pricing and a Super-Replication Theorem in a model-independent 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 payoff-function, e.g., a power option. This condition is not needed when sufficiently many vanilla options maturing at the horizon T are traded in the market.

Date: 2013-01, Revised 2013-03
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