Geodesic
Large financial markets, discounting, and no asymptotic arbitrage
Teoriâ veroâtnostej i ee primeneniâ, Tome 65 (2020) no. 2, pp. 237-280

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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 characterizations 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 “generalized martingale measures.” Our results extend the work of Rokhlin, Klein, and Schachermayer and Kabanov and Kramkov to a discounting-invariant framework. We also show how a market on $[0,\infty)$ 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 $[0,\infty)$.
Keywords: large financial markets, asymptotic arbitrage, discounting, no asymptotic arbitrage (NAA), no unbounded profit with bounded risk (NUPBR), asymptotic strong share maximality, dynamic share viability, asymptotic dynamic share viability, tradable discounter. 
D. A. Balint; M. Schweizer. Large financial markets, discounting, and no asymptotic arbitrage. Teoriâ veroâtnostej i ee primeneniâ, Tome 65 (2020) no. 2, pp. 237-280. http://geodesic.mathdoc.fr/item/TVP_2020_65_2_a1/
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