A MODEL‐FREE VERSION OF THE FUNDAMENTAL THEOREM OF ASSET PRICING AND THE SUPER‐REPLICATION THEOREM. (6th December 2013)

• Record Type: Journal Article
• Authors: Acciaio, B.; Beiglböck, M.; Penkner, F.; Schachermayer, W.
• Is Part Of: Mathematical finance. Volume 26:Number 2(2016:Apr.)
• Page Start: 233
• Page End: 251
• Publication Date: 2013-12-06
• Subjects: model‐independent pricing -- fundamental theorem of asset pricing -- super‐replication theorem; Business mathematics -- Periodicals; 332
• DOI: 10.1111/mafi.12060
• Languages: English
• ISSNs: 0960-1627

Abstract

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 superlinearly 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.