Results 13 resources
Arraut, I., Au, A., Tse, A. C., & Marques, J. A. L. (2020). On the probability flow in the Stock market I: The Black-Scholes case. ArXiv.Org, 1, 1–10. https://search.proquest.com/docview/2332255379?pq-origsite=primo
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.
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
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.
Arraut, I., Marques, J. A. L., Fong, S. J., Li, G., Gois, F. N. B., & Neto, J. X. (2022). A Quantum Field Formulation for a Pandemic Propagation. In J. A. L. Marques & S. J. Fong (Eds.), Epidemic Analytics for Decision Supports in COVID19 Crisis (pp. 141–158). Springer International Publishing. https://doi.org/10.1007/978-3-030-95281-5_6
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.
Marques, J. A. L., Fong, S. J., Li, G., Arraut, I., Gois, F. N. B., & Neto, J. X. (2022). Research and Technology Development Achievements During the COVID-19 Pandemic—An Overview. In J. A. L. Marques & S. J. Fong (Eds.), Epidemic Analytics for Decision Supports in COVID19 Crisis (pp. 1–15). Springer International Publishing. https://doi.org/10.1007/978-3-030-95281-5_1
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.
Arraut, I. (2023). The solution to the Hardy’s paradox (arXiv:2106.06397). arXiv. https://doi.org/10.48550/arXiv.2106.06397
By using both, the weak-value formulation as well as the standard probabilistic approach, we analyze the Hardy's experiment introducing a complex and dimensionless parameter ($\epsilon$) which eliminates the assumption of complete annihilation when both, the electron and the positron departing from a common origin, cross the intersection point $P$. We then find that the paradox does not exist for all the possible values taken by the parameter. The apparent paradox only appears when $\epsilon=1$; however, even in this case we can interpret this result as a natural consequence of the fact that the particles can cross the point $P$, but at different times due to a natural consequence of the energy-time uncertainty principle.
Arraut, I., Segovia, C., & Rosado, W. (2023). The Hawking Radiation in Massive Gravity: Path Integral and the Bogoliubov Method. Universe, 9(5), 228. https://doi.org/10.3390/universe9050228
We prove the consistency of the different approaches for deriving the black hole radiation for the spherically symmetric case inside the theory of Massive Gravity. By comparing the results obtained by using the Bogoliubov transformations with those obtained by using the Path Integral formulation, we find that in both cases, the presence of the extra-degrees of freedom creates the effect of extra-particles creation due to the distortions on the definitions of time defined by the different observers at large scales. This, however, does not mean extra-particle creation at the horizon level. Instead, the apparent additional particles perceived at large scales emerge from how distant observers define their time coordinate, which is distorted due to the existence of extra-degrees of freedom.
Arraut, I. (2023). Gauge symmetries and the Higgs mechanism in Quantum Finance (arXiv:2306.03237). arXiv. https://doi.org/https://doi.org/10.48550/arXiv.2306.03237
By using the Hamiltonian formulation, we demonstrate that the Merton-Garman equation emerges naturally from the Black-Scholes equation after imposing invariance (symmetry) under local (gauge) transformations over changes in the stock price. This is the case because imposing gauge symmetry implies the appearance of an additional field, which corresponds to the stochastic volatility. The gauge symmetry then imposes some constraints over the free-parameters of the Merton-Garman Hamiltonian. Finally, we analyze how the stochastic volatility gets massive dynamically via Higgs mechanism.
Arraut, J. M., Arraut, I., & Lei, K. I. (2023, July 3). Machine learning over the free-parameters of the Black-Scholes equation: Stock market and Option market. LatinX in AI Workshop at ICML 2023 (Regular Deadline). https://openreview.net/forum?id=e1pAJTU2Nh
The Black-Scholes equation is famous for predicting values for the prices of Options inside the stock market scenario. However, it has the limitation of depending on the estimated value for the volatility. On the other hand, several Machine learning techniques have been employed for predicting the values of the same quantity. In this paper we analyze some fundamental properties of the Black-Scholes equation and we then propose a way to train its free-parameters, the volatility in particular. This with the purpose of using this parameter as the fundamental one to be learned by a Machine Learning system and then improve the predictions in the stock market.
Banda, J. M., Ruiz-Garcia, A., Montoya, L. N., & Arraut, I. (2023). LatinX in AI research. Neural Computing and Applications, 35, 18097–18098. https://doi.org/10.1007/s00521-023-08790-9
We are delighted to present this special issue editorial for Neural Computing and Applications special issue on LatinX in AI research. This special issue brings together a collection of articles that explore machine learning and artificial intelligence research from various perspectives, aiming to provide a comprehensive and in-depth understanding of what LatinX researchers are working on in the field. In this editorial, we will introduce the overarching theme of the special issue, highlight the significance of the selected papers, and offer insights into the contributions made by the authors. The LatinX in AI organization was launched in 2018, with leaders from organizations in Artificial Intelligence, Education, Research, Engineering, and Social Impact with a purpose to together create a group that would be focused on “Creating Opportunity for LatinX in AI.” The main goal is to increase the representation of LatinX professionals in the AI industry. LatinX in AI Org and programs are volunteer-run and fiscally sponsored by the Accel AI Institute, 501(c)3 Non-Profit.
Arraut, I. (2023). Gauge symmetries and the Higgs mechanism in Quantum Finance. Europhysics Letters, 143(4), 42001. https://doi.org/10.1209/0295-5075/acedce
By using the Hamiltonian formulation, we demonstrate that the Merton-Garman equation emerges naturally from the Black-Scholes equation after imposing invariance (symmetry) under local (gauge) transformations over changes in the stock price. This is the case because imposing gauge symmetry implies the appearance of an additional field, which corresponds to the stochastic volatility. The gauge symmetry then imposes some constraints over the free parameters of the Merton-Garman Hamiltonian. Finally, we analyze how the stochastic volatility gets massive dynamically via Higgs mechanism.
Arraut, I. (2023). The Tully-Fisher law and dark matter effects derived via modified symmetries. Europhysics Letters, 144(2), 29003. https://doi.org/10.1209/0295-5075/ad05f7
In any physical system, when we move from short to large scales, new spacetime symmetries emerge which help us to simplify the dynamics of the system. In this letter we demonstrate that certain variations on the symmetries of general relativity at large scales generate the effects equivalent to dark matter ones. In particular, we reproduce the Tully-Fisher law, consistent with the predictions proposed by MOND. Additionally, we demonstrate that the dark matter effects derived in this way are consistent with the predictions suggested by MOND, without modifying gravity.
Arraut, I., & Lei, K.-I. (2023). The Role of the Volatility in the Option Market. AppliedMath, 3(4), 882–908. https://doi.org/10.3390/appliedmath3040047
We review some general aspects about the Black–Scholes equation, which is used for predicting the fair price of an option inside the stock market. Our analysis includes the symmetry properties of the equation and its solutions. We use the Hamiltonian formulation for this purpose. Taking into account that the volatility inside the Black–Scholes equation is a parameter, we then introduce the Merton–Garman equation, where the volatility is stochastic, and then it can be perceived as a field. We then show how the Black–Scholes equation and the Merton–Garman one are locally equivalent by imposing a gauge symmetry under changes in the prices over the Black–Scholes equation. This demonstrates that the stochastic volatility emerges naturally from symmetry arguments. Finally, we analyze the role of the volatility on the decisions taken by the holders of the options when they use the solution of the Black–Scholes equation as a tool for making investment decisions.
Rosado, W., & Arraut, I. (2023). Comment on “‘Generalized James’ effective Hamiltonian method”’. Physical Review A, 108(6), 066201. https://doi.org/10.1103/PhysRevA.108.066201
In the paper carried out by Wenjun et al. [Phys. Rev. A 95, 032124 (2017)], a generalization of the James effective dynamics theory based on a first version of the James method was presented. However, we contend that this is not a very rigorous way of deriving the effective third-order expansion for an interaction Hamiltonian with harmonic time-dependence. In fact, here we show that the third-order Hamiltonian obtained by Wenjun et al. is not Hermitian for general situations when we consider time dependence. Its non-Hermitian nature arises from the foundation of the theory itself. In this comment paper, the most general expression of the effective Hamiltonian expanded up to third order is obtained. Our derived effective Hamiltonian is Hermitian even in situations where we have time dependence.