  The main result of the paper is a version of the fundamental theorem of asset
pricing (FTAP) for large financial markets based on an asymptotic concept of no
market free lunch for monotone concave preferences. The proof uses methods from
the theory of Orlicz spaces. Moreover, various notions of no asymptotic
arbitrage are characterized in terms of no asymptotic market free lunch; the
difference lies in the set of utilities. In particular, it is shown directly
that no asymptotic market free lunch with respect to monotone concave utilities
is equivalent to no asymptotic free lunch. In principle, the paper can be seen
as the large financial market analogue of [Math. Finance 14 (2004) 351--357]
and [Math. Finance 16 (2006) 583--588].
