Financial markets are usually investigated through time series such as prices and volumes that describe the behavior of the system as a whole. Such observables emerge from microeconomic interactions between market participants. Agent-based models have been utilized to shed light on this process. The model's ability to produce statistics frequently found in empirical data is evidence of some correspondence with real markets. Here, an agent-based market model is proposed. Different trader profiles with short- and long-term motivations are considered, and limitations on the agents' skills to manipulate information are inserted into the model. According to their profile and limitations, agents are rational. A differential equation approximation is employed to find the value to which the price converges and the timescale of this process. The relationship between agents' attributes and the evolution of their wealth is explored in different scenarios. Agent's average wealth was not significantly affected by information processing accuracy, but the standard deviation was. The increased risk is the main consequence of low accuracy. The model yielded price series with multifractal behavior and heavy-tailed return distributions, which are nontrivial statistics frequently observed in empirical series.

Financial markets play a fundamental role in contemporary societies, directly influencing social well-being. Traditionally, economists have sought to understand the underlying processes driving the dynamics of these markets. However, in recent decades, there has been a significant increase in the contribution of researchers from various disciplines, including physics, mathematics, and computer science. In this context, econophysics has emerged, employing typical physics methods to study systems commonly investigated in economics and finance.Financial markets are recognized as complex systems, whose behavior can be observed through indicators such as prices and trading volumes. However, the statistical characterization of these time series remains an ongoing challenge, as does understanding their emergence from microeconomic relationships.The Efficient Market Hypothesis (EMH) suggests that future price time series in financial markets contain little useful information for prediction, making it extremely difficult. In this study, we conduct analyses of financial time series to investigate this expectation. We use a return trend prediction model based on differential equations with a focus on time segmenting. The accuracy of this model can provide insights into the presence of the information suggested by the EMH in financial time series.

Quantum relativistic solutions of a “square-root” version of the Klein–Gordon equation, for a particle in a one-dimensional Morse potential, are presented using methods previously proposed and applied to a particle in a harmonic oscillator. The methods lead to both numerical and analytical solutions, with the latter allowing smooth variation of the system parameters from non-relativistic to ultra-relativistic limits. Analytical expressions for the energy levels and wavefunctions are obtained, as solutions to a Schrödinger-type equation, including relativistic effects through a state-dependent rescaled mass. The eigenstates of the Morse potential exhibit suitable and smooth behavior and approach the corresponding harmonic oscillator solutions as the depth of the Morse potential well increases, as expected. A comparison is also presented between the relativistic harmonic oscillator obtained with this method and the so-called “Klein–Gordon oscillator”.

Um modelo baseado nas equações diferenciais que descrevem a dinâmica de um sistema físico composto por dois osciladores acoplados é apresentado para caracterizar séries de preços. A partir da discretização de tais equações, encontramos um modelo vetorial autorregressivo (VAR) de segunda ordem. Avaliamos o modelo nas séries de fechamento diários de duas ações relevantes do índice Ibovespa. A estacionariedade de tais séries foi averiguada pelo teste de Dickey-Fuller. Graficamente, verificamos que os resíduos resultantes da aplicação das séries no modelo não apresentam nenhum tipo de padrão.

Quantum relativistic solutions for a particle in a one-dimensional Morse potential are presented using methods previously proposed and applied to a particle in a harmonic oscillator. The methods lead to both numerical and analytical solutions, with the latter allowing smooth variation of the system parameters from non-relativistic to ultrarelativistic limits. Analytical expressions for the energy levels and wavefunctions are obtained, as solutions to a Schrödinger-type equation, including relativistic effects through a state dependent rescaled mass. The eigenstates of the Morse potential exhibit suitable and smooth behavior, and approach the corresponding harmonic oscillator solutions as the depth of the Morse potential well increases, as expected. A comparison is also presented between the relativistic harmonic oscillator obtained with this method, and the so-called Klein-Gordon oscillator.