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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.
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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.
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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.
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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.
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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.
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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.
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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.
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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.
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The Revenue Management (RM) problem in airlines for a fixed capacity, single resource and two classes has been solved before by using a standard formalism. In this paper we propose a model for RM by using the semi-classical approach of the Quantum Harmonic Oscillator. We then extend the model to include external factors affecting the people’s decisions, particularly those where collective decisions emerge.
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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.
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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.
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The primary research focus of this dissertation revolves around the concept of a "plugin" program. It raises a fundamental question about whether a building can attain long-term usability through metabolic flexibility (plugin units and their reconfigurable space), promoting adaptability (accommodating various program transfers), and meeting sustainable future criteria. Specifically, this dissertation inquires whether this "plugin" building design, with its reconfigurable units and metabolic system, can adapt to different spatial programs and become sustainable architecture
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This article presents an insight into one of the regions with the fastest-growing economy, heavily based on an entertainment, gaming and tourism industry, and that is urgently looking for a sustainable model that articulates with complementary sectors within the cultural and creative industries – Macao. Macao is facing a major economic and social challenge; it has grown as a vulnerable economy relying almost exclusively on gaming revenues. Alternative activities to diversify the economy are urgently required to answer the competition risks haunting this industry. The cultural and creative industries could be a complementary activity – a vehicle for economic diversification. However, current public and private stakeholders for the cultural and creative sector might have been neglecting the unique cultural and heritage ecosystem of the territory, focusing on isolate opportunities and overlooking an inclusive and robust strategy. A sustainable model that attends to the local conditions and its people is required for alternative activities to become a meaningful sector for the social and economic development of Macao.
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