Even simple observation of stock price graphs can reveal dominant patterns. In our work, we will refer to such re-occurring, dominant patterns as “coherent structures”, a term borrowed from the theory of turbulence in fluid dynamics. Stock price performance exhibits coherent structures, which by definition make it non-random, although a price-versus-time graph might seem totally chaotic to the naked eye. A novel low-order modeling technique for systems that are seemingly random has been developed. Though stock market data is used for the formulation and verification of the technique, its application in diverse fields is verified. The dissertation discusses some of the salient features of the novel technique along with a dynamic system analogy. The technique reduces many of the significant limitations associated with traditional methods like Fourier analysis and digital filters. Application of the technique to a nonlinear dynamical system and meteorological data are presented as well as the primary application on stock market securities.

The portfolio theory is microeconomic discipline which deals with the exploration of capital markets and assets that are traded on them. This diploma thesis is focused on optimal stock portfolio selection. The main aim is to find a final portfolio fulfilling the requirements. The first part provides the theory needed for the subsequent establishment of a practical case of the optimal portfolio. The second part is devoted to the actual calculations leading to finding the portfolio with the desired rate of return.

The diploma thesis focuses on the specification of suitability of legal entities to invest in securities "Exchange Traded Funds" in the current conditions of the Czech Republic. The results of the thesis serve to present alternative, modern ways to invest surplus money and get a new yield. Conclusions can be used by senior management of designated legal entities.