  Financial models based on the Wick product, and White Noise formalism have
previously been suggested in order to incorporate integrals with respect to
fractional Brownian motion. It has also been pointed out that this leads
naturally to a quantum mechanical interpretation of the financial market. In
this article we pursue this idea further, and in particular show how the
framework of quantum probability can be used to construct Martingales, without
relying on Brownian integrals. We go on to suggest benefits of doing so, and
avenues for future work.
