  Consider a single asset financial market whose discounted asset price process
is a stochastic integral with respect to a continuous regular strong Markov
semimartingale (a so-called general diffusion semimartingale) that is
parameterized by a scale function and a speed measure. In a previous paper, we
established a characterization of the no free lunch with vanishing risk (NFLVR)
condition for a canonical framework of such a financial market in terms of the
scale function and the speed measure. Ioannis Karatzas (personal communication)
asked us whether it is also possible to prove a characterization for the weaker
no unbounded profit with bounded risk (NUPBR) condition, which is the main
question we treat in this paper. Here, we do not restrict our attention to
canonical frameworks but we allow a general setup with a general filtration
that preserves the strong Markov property. Our main results are precise
characterizations of NUPBR and NFLVR which only depend on the scale function
and the speed measure. In particular, we prove that NUPBR forces the scale
function to be continuously differentiable with absolutely continuous
derivative. The latter extends our previous result, that, in the canonical
framework, NFLVR implies such a property, in two directions (a weaker
no-arbitrage notion and a more general framework). We also make the surprising
observation that NUPBR and NFLVR are equivalent whenever finite boundary points
are accessible for the driving diffusion.
