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

Voir la notice de l'article provenant de la source Math-Net.Ru

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. 
@article{TVP_2020_65_2_a1,
     author = {D. A. Balint and M. Schweizer},
     title = {Large financial markets, discounting, and no asymptotic arbitrage},
     journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
     pages = {237--280},
     publisher = {mathdoc},
     volume = {65},
     number = {2},
     year = {2020},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TVP_2020_65_2_a1/}
}
TY  - JOUR
AU  - D. A. Balint
AU  - M. Schweizer
TI  - Large financial markets, discounting, and no asymptotic arbitrage
JO  - Teoriâ veroâtnostej i ee primeneniâ
PY  - 2020
SP  - 237
EP  - 280
VL  - 65
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/TVP_2020_65_2_a1/
LA  - ru
ID  - TVP_2020_65_2_a1
ER  - 
%0 Journal Article
%A D. A. Balint
%A M. Schweizer
%T Large financial markets, discounting, and no asymptotic arbitrage
%J Teoriâ veroâtnostej i ee primeneniâ
%D 2020
%P 237-280
%V 65
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/item/TVP_2020_65_2_a1/
%G ru
%F TVP_2020_65_2_a1
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/