The Black-Scholes Equation and Certain Quantum Hamiltonians

Details The Black-Scholes Equation and Certain Quantum Hamiltonians The Black-Scholes Equation and Certain Quantum Hamiltonians

2010-02-08

arxiv.org/abs/1002.1667v2

International Journal of Pure and Applied Mathematics (IJPAM): Volume 67, No. 2 (2011)

Physics

Mathematical Physics

10 pages, no figures, some important changes were maked. An author was added. To appear in International Journal of Pure and A

Scientific paper

In this paper a quantum mechanics is built by means of a non-Hermitian momentum operator. We have shown that it is possible to construct two Hermitian and two non-Hermitian type of Hamiltonians using this momentum operator. We can construct a generalized supersymmetric quantum mechanics that has a dual based on these Hamiltonians. In addition, it is shown that the non-Hermitian Hamiltonians of this theory can be related to Hamiltonians that naturally arise in the so-called quantum finance.

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