In the modern version of Arbitrage Pricing Theory suggested by Kabanov and Kramkov the fundamental fi nancially meaningful concept is an asymptotic arbitrage. The 'real world' large market is represented by a sequence of 'models' and, though each of them is arbitrage free, investors may obtain...

In frictionless markets, the absence of arbitrage opportunities is equivalent to the existence of a martingale process evolving in the ray R_ S where S is the d-dimensional price process (whose first component is the numeraire). With transaction costs, absence of arbitrage opportunities is...

In contrast with the classical models of frictionless financial markets, market models with proportional transaction costs, even satisfying usual no-arbitrage properties, may admit arbitrage opportunities of the second kind. This means that there are self-financing portfolios with initial...

When dealing with non linear trading costs, e.g. fixed costs, the usual tools from convex analysis are inadequate to characterize an absence of arbitrage opportunity as the mathematical model is no more convex. An unified approach is to describe a financial market model by a liquidation value...

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 in terms of contiguity properties of sequences of equivalent probability measures induced by consistent...