Pseudo-Hermiticity and Removing Brownian Motion From Finance

In this article we apply the methods of quantum mechanics to the study of the financial markets. Specifically, we discuss the Pseudo-Hermiticity of the Hamiltonian operators associated to the typical partial differential equations of Mathematical Finance (such as the Black-Scholes equation) and how this relates to the non-arbitrage condition. We propose that one can use a Schrodinger equation to derive the probabilistic behaviour of the financial market, and discuss the benefits of doing so. This presents an alternative approach to replace the use of standard diffusion processes (for example a Brownian motion or Wiener process). We go on to study the method using the Bohmian approach to quantum mechanics. We consider how to interpret the equations for pseudo-Hermitian systems, and highlight the crucial role played by the quantum potential function.