Robust martingale selection problem and its connections to the no‐arbitrage theory. (17th July 2019)

• Record Type: Journal Article
• Authors: Burzoni, Matteo; Šikić, Mario
• Is Part Of: Mathematical finance. Volume 30:Number 1(2020)
• Page Start: 260
• Page End: 286
• Publication Date: 2019-07-17
• Subjects: arbitrage theory -- fundamental theorem of asset pricing -- illiquidity -- markets with frictions -- martingale selection problem; Business mathematics -- Periodicals; 332
• DOI: 10.1111/mafi.12225
• Languages: English
• ISSNs: 0960-1627

Abstract

Abstract: We analyze the martingale selection problem of Rokhlin in a pointwise (robust) setting. We derive conditions for solvability of this problem and show how it is related to the classical no‐arbitrage deliberations. We obtain versions of the Fundamental Theorem of Asset Pricing in models spanning frictionless markets, models with proportional transaction costs, and models for illiquid markets. In all these models, we also incorporate trading constraints.