A model-free version of the fundamental theorem of asset pricing and the super-replication theorem (Q2799994)

The authors consider a finite discrete-time setting and a market consisting of an arbitrary collection of options written on the same risky asset \(S\). A Fundamental Theorem of Asset Pricing (FTAP) and a Super-Replication Theorem (SPT) are proposed in a model-independent framework. More precisely, the following problems are addressed: Does there exist an arbitrage opportunity? For any additional option written on \(S\), what is the range of prices that do not create an arbitrage opportunity?NEWLINENEWLINEThese questions are exhaustively answered in the classical model-dependent framework, but in this paper they are studied without making any model assumption. Instead, the set of all models which are compatible with the prices observed in the market is considered. So, the authors follow the model-independent approach to financial mathematics. The concept of model-independent arbitrage is introduced via semi-static strategies. The existence of a traded option with a superlinearly growing payoff function is a technical condition, under which FTAP and SPT are established. Ramification of the super-replication result is also presented.