Most financial and investment decisions are based on considerations of possible future changes and require forecasts on the evolution of the financial world. Time series and processes are the natural tools for describing the dynamic behavior of financial data, leading to the required forecasts....

Despite being based on sound principles, the original Markowitz portfolio allocation theory cannot produce sound allocations, and restrictions or modifications need to be imposed from outside the theory in order to obtain meaningful portfolios. This is unsatisfactory, and the reasons for this...

Recent progresses in option pricing using ARCH processes for the underlying are summarized. The stylized facts are multiscale heteroscedasticity, fat-tailed distributions, time reversal asymmetry, and leverage. The process equations are based on a finite time increment, relative returns,...