Criteria for the absence of arbitrage in general diffusion markets

We establish deterministic necessary and sufficient conditions for the no-arbitrage notions NA (“no arbitrage”), NUPBR (“no unbounded profit with bounded risk”) and NFLVR (“no free lunch with vanishing risk”) in general diffusion market models with finite and infinite time horizons. These are single asset models whose (discounted) asset price process $Y$ is a regular continuous strong Markov process that is also a semimartingale. We further characterize the existence of an equivalent martingale measure in such models. All deterministic criteria are provided in terms of the scale function and the speed measure of $Y$.