ТЕОРЕТИЧНІ ТА МЕТОДИЧНІ АСПЕКТИ УПРАВЛІННЯ ІНВЕСТИЦІЙНИМ ПОРТФЕЛЕМ БАНКУ

Formulation of the problem. In modern conditions of globalization and volatility of financial markets, the investment activity of banks transforms from an auxiliary function into a strategic instrument. The key problem becomes the necessity of balancing between conflicting goals: maximization of profit, minimization of risks, and compliance with liquidity ratios under conditions of strict regulatory pressure. The purpose of the research consists in the systematization of theoretical and methodological approaches to the management of a bank's investment portfolio and the development of a generalized economic-mathematical model of its optimization, which takes into account specific constraints of banking activity. The object of the research is the processes of formation and management of the investment portfolio of a commercial bank. Methods used in the research: methods of theoretical generalization (for the analysis of the essence of the portfolio), comparative analysis (for the assessment of classical theories of Markowitz, Sharpe and modern approaches VaR, CVaR), as well as the toolkit of mathematical modeling and linear programming for the formalization of the optimization problem. The hypothesis of the research is based on the assumption that portfolio efficiency can be increased through the integration of classical efficiency indicators (Sharpe, Treynor, Sortino) with strict budget and regulatory constraints in a single optimization model. The statement of basic material. In the article, the evolution of approaches to the definition of the investment portfolio is analyzed and its key characteristics are highlighted: liquidity, reliability, profitability. A critical review of methods for assessing portfolio efficiency is carried out, in particular, the advantages and disadvantages of Sharpe, Treynor, Jensen, and Sortino coefficients are analyzed. The role of modern risk-oriented approaches (VaR, stress testing) is defined. The central element of the work is the economic-mathematical model of the linear programming problem constructed by the authors. The proposed model has an objective function of maximizing the total profitability of assets and includes an extended system of constraints: on the total volume of investments, fulfillment of liquidity ratios, permissible level of risk, and requirements of the bank's investment policy. The originality and practical significance of the research: a formalized model of portfolio structure optimization is developed, which, unlike standard solutions, allows taking into account constraints regarding liquidity and risk appetite specific to Ukrainian banks, ensuring scientifically grounded decision-making regarding asset rebalancing. Conclusions and perspectives of further research: the necessity of applying hybrid approaches combining the mathematical precision of optimization models with qualitative analysis of market conditions and regulatory requirements is confirmed.