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Generalizando a Mecânica Estatística de Boltzmann-Gibbs
Generalizando a Mecânica Estatística de Boltzmann-Gibbs
2019TsallisEscola.pdfEvidence for criticality in financial data
Evidence for criticality in financial data
1702.06191.pdfWe provide evidence that cumulative distributions of absolute normalized returns for the 100 American companies with the highest market capitalization, uncover a critical behavior for different time scales ∆t. Such cumulative distributions, in accordance with a variety of complex –and financial– systems, can be modeled by the cumulative distribution functions of q-Gaussians, the distribution function that, in the context of nonextensive statistical mechanics, maximizes a non-Boltzmannian entropy. These q-Gaussians are characterized by two parameters, namely (q, β), that are uniquely defined by ∆t. From these dependencies, we find a monotonic relationship between q and β, which can be seen as evidence of criticality. We numerically determine the various exponents which characterize this criticality. ial solvers
Economics and Finance: q-Statistical Stylized Features Galore
Economics and Finance: q-Statistical Stylized Features Galore
Tsallis - Entropia.pdfThe Boltzmann–Gibbs (BG) entropy and its associated statistical mechanics were generalized, three decades ago, on the basis of the nonadditive entropy Sq (q ∈ R), which recovers the BG entropy in the q → 1 limit. The optimization of Sq under appropriate simple constraints straightforwardly yields the so-called q-exponential and q-Gaussian distributions, respectively generalizing the exponential and Gaussian ones, recovered for q = 1. These generalized functions ubiquitously emerge in complex systems, especially as economic and financial stylized features. These include price returns and volumes distributions, inter-occurrence times, characterization of wealth distributions and associated inequalities, among others. Here, we briefly review the basic concepts of this q-statistical generalization and focus on its rapidly growing applications in economics and finance.
Econofísica: Dê um Control+F e procure por "Finance" no PDF abaixo:
Econofísica: Dê um Control+F e procure por "Finance" no PDF abaixo:
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