Pseudo-Hermiticity, Martingale Processes, and Non-Arbitrage Pricing

Abstract

In [2], and [13], financial models based on the Wick product, and White Noise formalism are suggested. Although the original purpose is to incorporate integrals with respect to fractional Brownian motion, it is also pointed out in these articles, 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.

Keywords: Quantum Probability, Black-Scholes

JEL Classification: C15,G13