ROBUST FUNDAMENTAL THEOREM FOR CONTINUOUS PROCESSES. (30th September 2015)

• Record Type: Journal Article
• Authors: Biagini, Sara; Bouchard, Bruno; Kardaras, Constantinos; Nutz, Marcel
• Is Part Of: Mathematical finance. Volume 27:Number 4(2017:Oct.)
• Page Start: 963
• Page End: 987
• Publication Date: 2015-09-30
• Subjects: fundamental theorem of asset pricing -- arbitrage of the first kind -- superhedging duality -- nondominated model; Business mathematics -- Periodicals; 332
• DOI: 10.1111/mafi.12110
• Languages: English
• ISSNs: 0960-1627

Abstract

Abstract: We study a continuous‐time financial market with continuous price processes under model uncertainty, modeled via a family P of possible physical measures. A robust notion NA 1 ( P ) of no‐arbitrage of the first kind is introduced; it postulates that a nonnegative, nonvanishing claim cannot be superhedged for free by using simple trading strategies. Our first main result is a version of the fundamental theorem of asset pricing: NA 1 ( P ) holds if and only if every P ∈ P admits a martingale measure that is equivalent up to a certain lifetime. The second main result provides the existence of optimal superhedging strategies for general contingent claims and a representation of the superhedging price in terms of martingale measures.