Before revision:  We obtain the equivalence of (a) the boundedness in probability of  wealth outcomes with (b) the existence of at least one deflator that make the deflated wealth processes have a generalized supermartingale property.
After revision:  We obtain the equivalence of the boundedness in probability of wealth outcomes with (b) the existence of at least one deflator that make the deflated wealth processes have a generalized supermartingale property.