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 .
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 .
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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
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
R
, 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)
. 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
R
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
suggest benefits of doing so, and avenues for future work