Nonlocal Diffusions and the Quantum Black-Scholes Equation: Modelling the Market Fear Factor

@article{Hicks2018NonlocalDA,
  title={Nonlocal Diffusions and the Quantum Black-Scholes Equation: Modelling the Market Fear Factor},
  author={William Hicks},
  journal={Risk Management \& Analysis in Financial Institutions eJournal},
  year={2018}
}
  • William Hicks
  • Published 6 June 2018
  • Mathematics
  • Risk Management & Analysis in Financial Institutions eJournal
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, Andreas Boukas, 'The Quantum Black-Scholes Equation', Jun 2007, available at arXiv:0706.1300v1) can be written in integral form. This enables the application of the Monte-Carlo methods adapted to McKean stochastic differential equations (H. P. McKean, 'A class of Markov processes associated with… 

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