A note on the condition of no unbounded profit with bounded risk

As a simple corollary to Delbaen and Schachermayer’s fundamental theorem of asset pricing [5] [6] [7], we prove, in a general finite-dimensional semimartingale setting, that the no unbounded profit with bounded risk (NUPBR) condition is equivalent to the existence of a strict martingale density for the price process. This extends the result of Choulli and Stricker [2] to the càdlàg cases, and refines partially the second main result of Karatzas and Kardaras [15] concerning the existence of an equivalent supermartingale deflator. The proof uses the technique of numéraire change.