IJPAM: Volume 90, No. 3 (2014)

SCHRÖDINGER GROUP AND QUANTUM FINANCE

Juan M. Romero$^1$, Ulises Lavana$^2$, Elio Martínez Miranda$^3$
$^{1,2}$Department of Applied Mathematics and Systems
UAM-Cuajimalpa
Artificios 40, México, D.F 01120, MEXICO
$^{3}$Facultad de Economía
Universidad Nacional Autónoma de México
México, D.F 04510, México


Abstract. Using the one dimensional free particle symmetries, the quantum finance symmetries are obtained. Namely, it is shown that Black-Scholes equation is invariant under Schrödinger group. In order to do this, the one dimensional free non-relativistic particle and its symmetries are revisited. To get the Black-Scholes equation symmetries, the particle mass is identified as the inverse of square of the volatility. Furthermore, using financial variables, a Schrödinger algebra representation is constructed.

Received: June 20, 2013

AMS Subject Classification: 81Q12, 91G80, 58D19

Key Words and Phrases: quantum physics, quantum finance, Schrödinger group

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DOI: 10.12732/ijpam.v90i3.3 How to cite this paper?
Source:
International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395
Year: 2014
Volume: 90
Issue: 3