Criteria for the absence of arbitrage in one-dimensional general diffusion markets

Abstract 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 one-dimensional general diffusion market models with finite and infinite time horizons. These are models whose (discounted) single risky asset price process $S$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>S</mml:mi> </mml:math> is a regular continuous strong Markov process that is also a semimartingale. We further characterise 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 $S$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>S</mml:mi> </mml:math> .