Absence of arbitrage revisited

The classic Black-Scholes model on an infinite horizon does not admit an equivalent martingale measure unless we already start with a martingale model. So it does not satisfy NFLVR. But in which sense is it still possibly... [ view full abstract ]

The classic Black-Scholes model on an infinite horizon does not admit an equivalent martingale measure unless we already start with a martingale model. So it does not satisfy NFLVR. But in which sense is it still possibly "arbitrage-free"? We provide a general analysis of this type of question on an open time interval for asset prices which are nonnegative semimartingales and whose sum never hits zero. Martingale-type characterisations and many explicit examples illustrate our approach.