Weak and strong no-arbitrage conditions for continuous financial markets

We propose a unified analysis of a whole spectrum of no-arbitrage conditions for finan- cial market models based on continuous semimartingales. In particular, we focus on no-arbitrage conditions weaker than the classical notions of No Arbitrage opportunity (NA) and No Free Lunch with Vanishing Risk (NFLVR). We provide a complete characterization of the considered no-arbitrage conditions, linking their validity to the characteristics of the discounted asset price process and to the existence and the properties of (weak) martingale deflators, and review classical as well as recent results.