The Black-Scholes Equation and Certain Quantum Hamiltonians
arXiv:1002.1667
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.
10 pages, no figures, some important changes were maked. An author was added. To appear in International Journal of Pure and Applied Mathematics-IJPAM