Analysing and modelling finance within nonextensive statistical mechanics formalism

Abstract

In this article we revisit results about financial quantities, namely return and traded volume, which have been obtained within the non-extensive statistical mechanics based on entropy. These results have been derived from both numerical (empirical) and analytical considerations. Concerning, the former, properties such as multi-fractality, self-correlation, and degree of dependence, have permitted not only the establishment of a basis for the application of nonextensivestatistical mechanics on the treatment of financial variables, but also the achievement of relations between typical statistical properties and entropic indices q . Pertaining to the latter, dynamical scenarios of differential stochastic equations have taken into account. In these cases, dynamical interpretations for index q have been presented.