Large Financial Markets, Discounting, and No Asymptotic Arbitrage

Dániel Ágoston Bálint and Martin Schweizer
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Dániel Ágoston Bálint: ETH Zurich - Department of Mathematics
Martin Schweizer: ETH Zurich; Swiss Finance Institute

No 18-70, Swiss Finance Institute Research Paper Series from Swiss Finance Institute

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 of suitably chosen “generalised martingale measures” along the sequence of small markets. 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; no asymptotic arbitrage; discounting; NAA; NUPBR; DIWV; ADIWV; tradable deflator (search for similar items in EconPapers)
JEL-codes: C00 G10 (search for similar items in EconPapers)
Pages: 35 pages
Date: 2018-11
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Persistent link: https://EconPapers.repec.org/RePEc:chf:rpseri:rp1870

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