Inspired by the theory of financial markets with transaction costs, we study a concept of essential supremum in the framework where a random partial order in Rd is lifted to the space L0(Rd) of d-dimensional random variables. In contrast to the classical definition, we define the essential...

In the first part of the paper, we study concepts of supremum and maximum as subsets of a topological space X endowed by preference relations. Several rather general existence theorems are obtained for the case where the preferences are defined by countable semicontinuous multi-utility...

<Para ID="Par1">We give characterizations of asymptotic arbitrage of the first and second kind and of strong asymptotic arbitrage for a sequence of financial markets with small proportional transaction costs λ <Subscript> n </Subscript> on market n, in terms of contiguity properties of sequences of equivalent probability measures...</subscript></para>

This paper proves the fundamental theorem of asset pricing with transaction costs, when bid and ask prices follow locally bounded càdlàg (right-continuous, left-limited) processes. The robust no free lunch with vanishing risk condition (RNFLVR) for simple strategies is equivalent to the...