English

The Black-Scholes Equation and Certain Quantum Hamiltonians

Mathematical Physics 2011-03-25 v2 High Energy Physics - Theory math.MP Quantum Physics

Abstract

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.

Keywords

Cite

@article{arxiv.1002.1667,
  title  = {The Black-Scholes Equation and Certain Quantum Hamiltonians},
  author = {Juan M. Romero and O. Gonzalez-Gaxiola and J. Ruiz de Chavez and R. Bernal-Jaquez},
  journal= {arXiv preprint arXiv:1002.1667},
  year   = {2011}
}

Comments

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

R2 v1 2026-06-21T14:44:41.089Z