Making predictions for future events is one of the most interesting research topic in many areas of social-and natural sciences. The aim of this talk is to present some of the author’s work and results in that direction by applying several techniques of mathematical modelling, optimization and predictive analytics. By using different linear algebraic rating methods to evaluate the relative performance of sport teams round by round we assign probabilities for the possible outcomes of the upcoming matches. We empirically estimate the predictive power of the method comparing it to the widely-used Bradley-Terry model and also to the forecasts of experts using bookmaker's betting odds data. Then, we investigate the portfolio selection problem, which is one of the most important problem in asset management, aims at reducing the risk of an investment by diversifying it into independently fluctuating assets.

We apply different filtering procedures (Random Matrix Theory, Clustering) to the correlation matrices obtained by Budapest Stock Exchange data. Our results show that estimated risk is much closer to the realized risk of a portfolio using filtering methods. Bootstrap analysis shows that ratio between the realized return and the estimated risk (Sharpe ratio) is also improved by filtering.