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

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...

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Autores principales:	Ivan Arraut, João Alexandre Lobo Marques, Sergio Gomes
Formato:	article
Lenguaje:	EN
Publicado:	MDPI AG 2021
Materias:	martingale condition vacuum condition spontaneous symmetry breaking degenerate vacuum flow of information Hermiticity Mathematics QA1-939
Acceso en línea:	https://doaj.org/article/bb62b69a9a7d45ba9fb7ce85eff42077
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spelling	oai:doaj.org-article:bb62b69a9a7d45ba9fb7ce85eff420772021-11-11T18:19:09ZThe Probability Flow in the Stock Market and Spontaneous Symmetry Breaking in Quantum Finance10.3390/math92127772227-7390https://doaj.org/article/bb62b69a9a7d45ba9fb7ce85eff420772021-11-01T00:00:00Zhttps://www.mdpi.com/2227-7390/9/21/2777https://doaj.org/toc/2227-7390The 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.Ivan ArrautJoão Alexandre Lobo MarquesSergio GomesMDPI AGarticlemartingale conditionvacuum conditionspontaneous symmetry breakingdegenerate vacuumflow of informationHermiticityMathematicsQA1-939ENMathematics, Vol 9, Iss 2777, p 2777 (2021)
institution	DOAJ
collection	DOAJ
language	EN
topic	martingale condition vacuum condition spontaneous symmetry breaking degenerate vacuum flow of information Hermiticity Mathematics QA1-939
spellingShingle	martingale condition vacuum condition spontaneous symmetry breaking degenerate vacuum flow of information Hermiticity Mathematics QA1-939 Ivan Arraut João Alexandre Lobo Marques Sergio Gomes The Probability Flow in the Stock Market and Spontaneous Symmetry Breaking in Quantum Finance
description	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.
format	article
author	Ivan Arraut João Alexandre Lobo Marques Sergio Gomes
author_facet	Ivan Arraut João Alexandre Lobo Marques Sergio Gomes
author_sort	Ivan Arraut
title	The Probability Flow in the Stock Market and Spontaneous Symmetry Breaking in Quantum Finance
title_short	The Probability Flow in the Stock Market and Spontaneous Symmetry Breaking in Quantum Finance
title_full	The Probability Flow in the Stock Market and Spontaneous Symmetry Breaking in Quantum Finance
title_fullStr	The Probability Flow in the Stock Market and Spontaneous Symmetry Breaking in Quantum Finance
title_full_unstemmed	The Probability Flow in the Stock Market and Spontaneous Symmetry Breaking in Quantum Finance
title_sort	probability flow in the stock market and spontaneous symmetry breaking in quantum finance
publisher	MDPI AG
publishDate	2021
url	https://doaj.org/article/bb62b69a9a7d45ba9fb7ce85eff42077
work_keys_str_mv	AT ivanarraut theprobabilityflowinthestockmarketandspontaneoussymmetrybreakinginquantumfinance AT joaoalexandrelobomarques theprobabilityflowinthestockmarketandspontaneoussymmetrybreakinginquantumfinance AT sergiogomes theprobabilityflowinthestockmarketandspontaneoussymmetrybreakinginquantumfinance AT ivanarraut probabilityflowinthestockmarketandspontaneoussymmetrybreakinginquantumfinance AT joaoalexandrelobomarques probabilityflowinthestockmarketandspontaneoussymmetrybreakinginquantumfinance AT sergiogomes probabilityflowinthestockmarketandspontaneoussymmetrybreakinginquantumfinance
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The Probability Flow in the Stock Market and Spontaneous Symmetry Breaking in Quantum Finance

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