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