For several decades, the no-arbitrage (NA) condition and the martingale measures have played a major role in the financial asset's pricing theory. Here, we propose a new approach based on convex duality instead of martingale measures duality: our prices will be expressed using Fenchel conjugate...

This paper proves the Fundamental Theorem of Asset Pricing with transaction costs, when bid and ask prices follow locally bounded cadlag (right-continuous, left-limited) processes. The Robust No Free Lunch with Vanishing Risk (RNFLVR) condition for simple strategies is equivalent to the...

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...

We study how trading costs are reflected in equilibrium returns. To this end, we develop a tractable continuous-time risk-sharing model, where heterogeneous mean-variance investors trade subject to a quadratic transaction cost. The corresponding equilibrium is characterized as the unique...