Maximum entropy models for financial systems

Abstract

Complex systems, from financial markets to the brain, exhibit heterogeneous

structures and non-stationary dynamics. These characteristics manifest themselves in the diversity of the elements in a system, and in the changing behaviour over time. Capturing and understanding this heterogeneity via appropriate models, can have important implications not only for science, but also for societal challenges like predicting the next financial crisis or developing advanced brain imaging techniques. In this thesis, we use the maximum-entropy approach to introduce a new class of statistical models, which captures part of the observed

structural and/or temporal heterogeneity in the system. The models are applied to various real-world complex systems, and are used to address different problems.