Banca de DEFESA: LUCIENE LOPES BORGES MIRANDA

Uma banca de DEFESA de DOUTORADO foi cadastrada pelo programa.
STUDENT : LUCIENE LOPES BORGES MIRANDA
DATE: 30/11/2023
TIME: 14:00
LOCAL: Videoconferência
TITLE:

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KEY WORDS:

Itô calculations; Financial Market, White Noise, Time Series

PAGES: 84
BIG AREA: Outra
AREA: Multidisciplinar
SUMMARY:

The complexity of behavior and studies on the financial market and the Itô-Langevin Calculations, become an attractive field of studies for researchers in several areas, such as: Economics, Systems Analysis, Mathematics and Physics. We can emphasize its importance for such studies in interdisciplinary areas, such as: Econophysics, which relate elements of Economics and Physics in the study of markets and financial systems. Statistical mechanics is one of the main tools for modeling these financial systems, more precisely the price dynamics. To understand such facts, the Itô stochastic differential equations were used, with additive white noise as a mathematical model for the price dynamics of the financial market. Mathematical methods of Statistical Physics have been applied in the description of economic systems to time series to investigate the behavior of financial markets at different scales. Among the tools used for this, are measures of central dispersion, probability distribution, stochastic dynamics, and methods to estimate the correlations. Financial instruments such as assets, options and stock exchange indices fluctuate over time, so they can be modeled by stochastic processes. In this way this thesis intends to verify if a stochastic differential equation (interfered by white and non-white noise) attend a stylized fact of the market. More specifically, if the heavy tail of the distribution of absolute returns generated by the proposed equation follows an empirical power law. Furthermore, we estimate the Hurst exponent through R/S Analysis and DFA to verify the long-range dependence, or long memory of the obtained time series. As the noise term that composes the equation is non-differentiable, we introduce the stochastic calculus to analytically obtain its solution.

COMMITTEE MEMBERS:
Interno - GIANCARLO QUEIROZ PELLEGRINO
Presidente - LEONARDO DOS SANTOS LIMA
Externo à Instituição - LEONARDO FERREIRA CALAZANS
Externo ao Programa - LUIS ARGEL POVEDA CALVINO
Interno - THIAGO DE SOUZA RODRIGUES
Interno - THIAGO GOMES DE MATTOS