Closed Quantum Black-Scholes: Quantum Drift and the Heisenberg Equation of Motion

@article{Hicks2020ClosedQB,
  title={Closed Quantum Black-Scholes: Quantum Drift and the Heisenberg Equation of Motion},
  author={William Hicks},
  journal={Risk Management eJournal},
  year={2020}
}
  • William Hicks
  • Published 26 November 2019
  • Physics
  • Risk Management eJournal
In this article we model a financial derivative price as an observable on the market state function. We apply geometric techniques to integrating the Heisenberg Equation of Motion. We illustrate how the non-commutative nature of the model introduces quantum interference effects that can act as either a drag or a boost on the resulting return. The ultimate objective is to investigate the nature of quantum drift in the Accardi-Boukas quantum Black-Scholes framework which involves modelling the… 
Wild Randomness and the Application of Hyperbolic Diffusion in Financial Modelling
The application of the Cauchy distribution has often been discussed as a potential model of the financial markets. In particular the way in which single extreme, or "Black Swan", events can impact

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TLDR
It is shown how certain nonlocal diffusions can be written as quantum stochastic processes, and how one can use path integral formalism, and PT symmetric quantum mechanics, to build a non-Gaussian kernel function for the Accardi–Boukas quantum Black–Scholes.
Nonlocal Diffusions and the Quantum Black-Scholes Equation: Modelling the Market Fear Factor
  • William Hicks
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In this paper, we establish a link between quantum stochastic processes, and nonlocal diffusions. We demonstrate how the non-commutative Black-Scholes equation of Accardi & Boukas (Luigi Accardi,
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