arXiv:1002.1667

The Black-Scholes Equation and Certain Quantum Hamiltonians

Juan M. Romero, Oswaldo Gonzalez-Gaxiola, J. Ruiz de Chávez, Roberto Bernal-Jaquez

Published Feb 8, 2010• 8 citations

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.

DOI: 10.48550/arxiv.1002.1667

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