One goal of this work is to provide an overview of the development trends of quantitative methods and models in capital market theory and the practice of investment analysis. Starting from the well-known classical capital market models, more recent nonlinear and dynamic concepts are presented. Even very simple nonlinear dynamic models exhibit movement patterns in their temporal development that can be considered typical for price developments of assets in capital markets. Numerous recent models for describing stock price developments include the potential for dynamic behavior that can be both stable and periodic, as well as irregular and erratic. The work focuses on the conditions for these phenomena, their manifestations, and the implications for capital market theory and investment analysis.