The Probability Flow in the Stock Market and Spontaneous Symmetry Breaking in Quantum Finance

Resource type
Authors/contributors
Title
The Probability Flow in the Stock Market and Spontaneous Symmetry Breaking in Quantum Finance
Abstract
The spontaneous symmetry breaking phenomena applied to Quantum Finance considers that the martingale state in the stock market corresponds to a ground (vacuum) state if we express the financial equations in the Hamiltonian form. The original analysis for this phenomena completely ignores the kinetic terms in the neighborhood of the minimal of the potential terms. This is correct in most of the cases. However, when we deal with the martingale condition, it comes out that the kinetic terms can also behave as potential terms and then reproduce a shift on the effective location of the vacuum (martingale). In this paper, we analyze the effective symmetry breaking patterns and the connected vacuum degeneracy for these special circumstances. Within the same scenario, we analyze the connection between the flow of information and the multiplicity of martingale states, providing in this way powerful tools for analyzing the dynamic of the stock markets.
Publication
Mathematics
Volume
9
Issue
21
Pages
2777
Date
2021/1
Language
en
DOI
10.3390/math9212777
ISSN
2227-7390
Accessed
4/11/23, 2:03 PM
Library Catalog
Extra
Number: 21 Publisher: Multidisciplinary Digital Publishing Institute
Citation
Arraut, I., Lobo Marques, J. A., & Gomes, S. (2021). The Probability Flow in the Stock Market and Spontaneous Symmetry Breaking in Quantum Finance. Mathematics, 9(21), 2777. https://doi.org/10.3390/math9212777