Semimartingales and asset pricing under constraints

We extend the well known fundamental theorem of asset pricing to the case of security markets models with frictions. We provide necessary and sufficient conditions for the existence of martingale, supermartingale and quasimartingale laws equivalent to the reference one. These conditions have a natural interpretation as no free lunch conditions in financial markets models with frictions. In this context we also show that an adapted stochastic process is a semimartingale if and only if no-extreme-arbitrage opportunities are allowed.