Integrais de caminho e o índice Ibovespa

Abstract

Due it to the new development of econophysics, a field of physics that deal with economical problems, it became possible to apply some of the tools used in quantum field theory to solve many problems in economics and finance, as well as to use them to better understand the phenomena in economical systems. Our goal in this work is to use those tools to search for a new understanding about the evolution of economical indexes and the capability to predict them, as we will see, for example, in the Ibovespa index of Brazilian stock market. Among those useful tools of quantum field theory the most important one are the path integral. Due to the high applicability, they are used in several physical theories, especially in field theories at finite temperature and in the study of non-equilibrium phenomena. The issue is based on theories that deal with non-equilibrium phenomena, we will present in this work a path integral formalism that allows us to write the transition probability between two different points of stochastic process and relate it with a wellknown probability density function: the truncated Lévy flights. This transition probability is applied to predict the returns of the Ibovespa index of the Brazilian stock market with a good agreement between the theoretic prediction and the historical data obtained from Bovespa.