Asymptotic arbitrage in noncomplete large financial markets

Abstract

Kabanov and Kramkov introduced the notion of "large financial markets." Instead of considering - as usual in mathematical finance - a stochastic stock price process S based on a filtered probability space (Ω, ℱ, (ℱt)t∈Il>, P) one considers a sequence (Sn)n=1 of such processes based on a sequence (Ωn, ℱn, (ℱnt)t∈In, Pn)n=1 of filtered probability spaces. The interpretation is that an investor can invest not only in one stock exchange but in several (in the model countably many) stock exchanges. The usual notion of arbitrage may then be interpreted by "asymptotic's" arbitrage concepts, where it is essential to distinguish between two different kinds introduced by Kabanov and Kramkov.