In the modern version of Arbitrage Pricing Theory suggested by Kabanov and Kramkov the fundamental financially meaningful concept is an asymptotic arbitrage. The “real” large market is represented by a sequence of “models” and, though each of them is arbitrage free, investors may obtain non–risky profits in the limit. Mathematically, absence of the asymptotic arbitrage is expressed as contiguity of envelopes of the sets of equivalent martingale measures and objective probabilities. The classical theory deals with frictionless markets. We extend it to markets with transaction costs. Assuming that each model admits consistent price systems, we relate them with families of probability measures and consider their upper and lower envelopes. The main result concerns the necessary and sufficient conditions for absence of asymptotic arbitrage opportu-nities of the first and second kinds expressed in terms of contiguity. We provide also more specific conditions involving Hellinger processes and give applications to particular models of large financial markets.
Keywords: Transaction Costs; Large financial markets; Asymptotic arbitrage; Contiguity
Biography: Emmanuel DENIS is assistant professor at Paris Dauphine University. His main research interests in Mathematical finance are: Arbitrage theory and Approximated hedging in presence of transaction costs.