On the probability flow in the Stock market I: The Black-Scholes case - Arraut, Ivan; Au, Alan; Tse, Alan Ching-biu; Marques, Joao Alexandre Lobo (arXiv.org, 2020)
It is known that the probability is not a conserved quantity in the stock market, given the fact that it corresponds to an open system. In this paper we analyze the flow of probability in this system by expressing the ideal Black-Scholes equation in the Hamiltonian form. We then analyze how the non-conservation of probability affects the stability of the prices of the Stocks. Finally, we find the conditions under which the probability might be conserved in the market, challenging in this way the non-Hermitian nature of the Black-Scholes Hamiltonian.
Place: Ithaca, United States Publisher: Cornell University Library, arXiv.org Section: Quantitative Finance University: Cornell University Library arXiv.org
Keywords: General Finance

The Probability Flow in the Stock Market and Spontaneous Symmetry Breaking in Quantum Finance - Arraut, Ivan; Lobo Marques, João Alexandre; Gomes, Sergio (Mathematics, 2021)
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.
Number: 21 Publisher: Multidisciplinary Digital Publishing Institute
Keywords: Hermiticity; conservation of the information; degenerate vacuum; flow of information; martingale condition; random fluctuations; spontaneous symmetry breaking; vacuum condition

A Quantum Field Formulation for a Pandemic Propagation - Arraut, Ivan; Marques, João Alexandre Lobo; Fong, Simon James; Li, Gloria; Gois, Francisco Nauber Bernardo; Neto, José Xavier (Epidemic Analytics for Decision Supports in COVID19 Crisis, 2022)
In this chapter, a mathematical model explaining generically the propagation of a pandemic is proposed, helping in this way to identify the fundamental parameters related to the outbreak in general. Three free parameters for the pandemic are identified, which can be finally reduced to only two independent parameters. The model is inspired in the concept of spontaneous symmetry breaking, used normally in quantum field theory, and it provides the possibility of analyzing the complex data of the pandemic in a compact way. Data from 12 different countries are considered and the results presented. The application of nonlinear quantum physics equations to model epidemiologic time series is an innovative and promising approach.
Keywords: COVID-19; Mathematical modeling; Nonlinear analysis; Quantum field theory

Research and Technology Development Achievements During the COVID-19 Pandemic—An Overview - Marques, João Alexandre Lobo; Fong, Simon James; Li, G.; Arraut, Ivan; Gois, F. Nauber Bernardo; Neto, José Xavier (Epidemic Analytics for Decision Supports in COVID19 Crisis, 2022)
At the beginning of 2020, the World Health Organization (WHO) started a coordinated global effort to counterattack the potential exponential spread of the SARS-Cov2 virus, responsible for the coronavirus disease, officially named COVID-19. This comprehensive initiative included a research roadmap published in March 2020, including nine dimensions, from epidemiological research to diagnostic tools and vaccine development. With an unprecedented case, the areas of study related to the pandemic received funds and strong attention from different research communities (universities, government, industry, etc.), resulting in an exponential increase in the number of publications and results achieved in such a small window of time. Outstanding research cooperation projects were implemented during the outbreak, and innovative technologies were developed and improved significantly. Clinical and laboratory processes were improved, while managerial personnel were supported by a countless number of models and computational tools for the decision-making process. This chapter aims to introduce an overview of this favorable scenario and highlight a necessary discussion about ethical issues in research related to the COVID-19 and the challenge of low-quality research, focusing only on the publication of techniques and approaches with limited scientific evidence or even practical application. A legacy of lessons learned from this unique period of human history should influence and guide the scientific and industrial communities for the future.
Keywords: COVID-19; Research cooperation; Research ethics; Scientific research; Technology development