Multivariate maximum entropy densities applied for multivariate analysis of financial time series

This dissertation discusses the construction of multivariate maximum entropy density using various entropy measures such as Tsallis’ entropy and Kapur’s entropy. By imposing certain restrictions on the maximization, the new models are able to capture multivariate distributional stylized facts often found in bivariate financial return series, including asymmetry, fat-tails and correlation. The concepts and properties of the new class of models are introduced in comparison with the conventional parametric distributions. The algorithm yielding the density and some empirical studies are also given in the thesis.