  We analyze the martingale selection problem of Rokhlin (2006) 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 examples spanning
frictionless markets, models with proportional transaction costs and also
models for illiquid markets. In all these examples, we also incorporate trading
constraints.
