Quantitative Analysis of Financial Instruments Based on Portfolio Theory and Game Theory

The article focuses on modern methods of quantitative analysis of financial instruments based on the Markowitz portfolio theory, which allows designing optimal portfolios of financial instruments under the assumption of extreme rationality of investors and game theory, which allows taking into account the factor of player interaction between those participating in financial markets. The relevance of the research topic concerns the need to improve the quality of financial decisions made in conditions of increased volatility of financial markets. An initial set of financial instruments was built, consisting of fifty alternative options for placing funds. A preliminary analysis of the initial set of financial instruments allowed us to narrow it down to ten elements that are most preferable for placing funds. The classic Markowitz portfolio model, which assumes maximizing the expected return on a portfolio at a given level of risk, is complemented by auxiliary constraints that allow taking into account individual investor preferences. The presented six modifications of Markowitz portfolios help to identify the dynamics of the quantitative characteristics of portfolios depending on the individual preferences of investors. Expected profitability and expected risk, estimated from real financial data, are accepted as quantitative characteristics of portfolios. The game model is constructed in the form of a game with nature, which allows taking into account the complex nature of player interaction, which in most cases is not characterized by antagonism. The game model is designed to select the optimal net strategy of the investor, which takes into account various financial market conditions expressed by a market index (market portfolio). The study of the game model is implemented on the basis of the integrated Hodge-Lehman criterion regarding profitability and risk. Its use made it possible to take into account the individual level of investor confidence in the available financial information. In the process of practical implementation of these techniques, results were obtained that allow us to conclude about the degree of sensitivity of optimal investment strategies to individual preferences and perceptions of investors. The constructed models can be used to update the content of professional training of students in the higher economic school system, as well as to set up courses of additional professional education.