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Pseudo Hermitian formulation of the quantum Black–Scholes Hamiltonian

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  • Jana, T.K.
  • Roy, P.

Abstract

We show that the non-Hermitian Black–Scholes Hamiltonian and its various generalizations are η-pseudo Hermitian. The metric operator η is explicitly constructed for this class of Hamiltonians. It is also shown that the effective Black–Scholes Hamiltonian and its partner form a pseudo supersymmetric system.

Suggested Citation

  • Jana, T.K. & Roy, P., 2012. "Pseudo Hermitian formulation of the quantum Black–Scholes Hamiltonian," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 391(8), pages 2636-2640.
    • Handle: RePEc:eee:phsmap:v:391:y:2012:i:8:p:2636-2640
    DOI: 10.1016/j.physa.2011.12.012
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    References listed on IDEAS

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    1. Mantegna,Rosario N. & Stanley,H. Eugene, 2007. "Introduction to Econophysics," Cambridge Books, Cambridge University Press, number 9780521039871.
    2. Kirill Ilinski, 1997. "Physics of Finance," Papers hep-th/9710148, arXiv.org.
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    Cited by:

    1. Will Hicks, 2020. "Pseudo-Hermiticity, Martingale Processes and Non-Arbitrage Pricing," Papers 2009.00360, arXiv.org, revised Apr 2021.
    2. Will Hicks, 2021. "Wild Randomness, and the application of Hyperbolic Diffusion in Financial Modelling," Papers 2101.04604, arXiv.org, revised Apr 2021.

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