Robust martingale selection problem and its connections to the no-arbitrage theory

Abstract

We analyze the martingale selection problem of Rokhlin in a pointwise (robust) setting. We derive conditions for solvability of this problem and show how it is related to the classical no-arbitrage deliberations. We obtain versions of the Fundamental Theorem of Asset Pricing in models spanning frictionless markets, models with proportional transaction costs, and models for illiquid markets. In all these models, we also incorporate trading constraints.