An alternative proof of a result of Takaoka

In Karatzas and Kardaras’s paper [11] it is proved that the NUPBR condition is a property of the local characteristic of the asset process. In Takaoka’s paper [15] it is proved that the NUPBR condition is equivalent to the existence of a local martingale deflator. However, the paper [15] founds its proof on Delbaen and Schachermayer’s fundamental asset pricing theorem, i.e. the NFLVR condition, which is not a pure property of the local characteristic of the asset process, as shown in [11]. In this paper we give an alternative proof of the result of [15] which makes use only the properties of the local characteristic of the asset process. This proof complete the program initiated in [11] which establishes an autonomous theory for the NUPBR condition.