The article proposes a complex of economic and mathematical models of assessment, analysis, and forecasting of the world stock indices development state for effective management of investment flows. The modern concept and strategy of European countries’ stock market development were considered, and the existing methods of diagnosing the stock market development level were analyzed. ARIMA models were built and spectral analysis of the main world indices was carried out. The possible trends in the stock indices development for the future period were analyzed using predictive models. It makes it possible to determine directions for improving the stock market efficiency and investment strategies in modern conditions.The proposed set of models for evaluation, analysis, and forecasting of the world stock indices state can be used to test various trading strategies and to test various hypotheses in relation to the entire stock portfolio of a particular company or to one stock index. The results of the research can be used in the development of theoretical provisions and methodological tools for evaluating the global stock market effectiveness in modern conditions and development trends in local markets.