Before revision:  We provide a complete characterisation of all no-arbitrage conditions, linking their validity to the existence and to the  properties of (weak) martingale deflators and to the characteristics of the discounted asset price process .
After revision:  We provide a complete characterisation of the considered no-arbitrage conditions, linking their validity to the existence and to the properties of (weak) martingale deflators and to the characteristics of the discounted asset price process .