Large Financial Markets, Discounting, and No Asymptotic Arbitrage

Bálint, Dániel Ágoston; Schweizer, Martin

doi:10.2139/ssrn.3280855

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Large Financial Markets, Discounting, and No Asymptotic Arbitrage

Swiss Finance Institute Research Paper No. 18-70

37 Pages Posted: 9 Nov 2018 Last revised: 21 Apr 2020

See all articles by Dániel Ágoston Bálint

Martin Schweizer

ETH Zurich; Swiss Finance Institute

Date Written: November 7, 2018

Abstract

For a large financial market (which is a sequence of usual, “small” financial markets), we introduce and study a concept of no asymptotic arbitrage (of the first kind) which is invariant under discounting. We give two dual characterisations of this property in terms of (1) martingale-like properties for each small market plus (2) a contiguity property, along the sequence of small markets, of suitably chosen “generalised martingale measures”. Our results extend the work of Rokhlin and of Klein/Schachermayer and Kabanov/Kramkov to a discounting-invariant framework. We also show how a market on [0,∞) can be viewed as a large financial market and how no asymptotic arbitrage, both classic and in our new sense, then relates to no-arbitrage properties directly on [0,∞).

Keywords: large financial markets, asymptotic arbitrage, discounting, NAA, NUPBR, asymptotic strong share maximality, dynamic share viability, asymptotic dynamic share viability, tradable discounter

JEL Classification: C00, G10

Suggested Citation: Suggested Citation

Bálint, Dániel Ágoston and Schweizer, Martin, Large Financial Markets, Discounting, and No Asymptotic Arbitrage (November 7, 2018). Swiss Finance Institute Research Paper No. 18-70, Available at SSRN: https://ssrn.com/abstract=3280855 or http://dx.doi.org/10.2139/ssrn.3280855