Making no-arbitrage discounting-invariant: a new FTAP beyond NFLVR and NUPBR

40 Pages Posted: 19 Aug 2020

See all articles by Dániel Ágoston Bálint

Dániel Ágoston Bálint

ETH Zürich - Department of Mathematics

Martin Schweizer

ETH Zurich; Swiss Finance Institute

Multiple version iconThere are 2 versions of this paper

Date Written: July 10, 2020


In the simplest formulation, this paper addresses the following question: Given two positive asset prices on a right-open interval, how can one decide, in an economically natural manner, whether or not this is an arbitrage-free model?
In general multi-asset models of financial markets, the classic notions NFLVR and NUPBR depend crucially on how prices are discounted. To avoid such issues, we introduce a discounting-invariant absence-of-arbitrage concept. Like in earlier work, this rests on zero or some basic strategies being 'maximal'; the novelty is that maximality of a strategy is defined in terms of 'share' holdings instead of 'value'. This allows us to generalise both NFLVR, by dynamic share efficiency, and NUPBR, by dynamic share viability. These concepts are the same for discounted or undiscounted prices, and they can be used in open-ended models under minimal assumptions on asset prices. We establish corresponding versions of the FTAP, i.e., dual characterisations in terms of martingale properties. As one expects, “properly anticipated prices fluctuate randomly”, but with an 'endogenous' discounting process which must not be chosen a priori. The classic Black–Scholes model on [0,∞) is arbitrage-free in this sense if and only if its parameters satisfy m−r ∈ {0, σ²} or, equivalently, either bond-discounted or stock-discounted prices are martingales.

Keywords: absence of arbitrage, maximal strategies, semimartingales, discounting, NFLVR, NUPBR, FTAP, -martingale discounter, strongly share maximal, dynamic share viability, Black–Scholes model

JEL Classification: C00, G10

Suggested Citation

Bálint, Dániel Ágoston and Schweizer, Martin, Making no-arbitrage discounting-invariant: a new FTAP beyond NFLVR and NUPBR (July 10, 2020). Swiss Finance Institute Research Paper No. 18-23_ Version 2, Available at SSRN: or

Dániel Ágoston Bálint

ETH Zürich - Department of Mathematics ( email )

R¨amistrasse 101
Raemistr. 101
Z¨urich, 8092

Martin Schweizer (Contact Author)

ETH Zurich ( email )

Mathematik, HG G51.2
Raemistrasse 101
CH-8092 Zurich

Swiss Finance Institute

c/o University of Geneva
40, Bd du Pont-d'Arve
CH-1211 Geneva 4

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