ЄФЕКТИВНА ДИВЕРСИФІКАЦІЯ ТА ДИНАМІКА ПОРТФЕЛЯ АКЦІЙ ЗА УМОВ ОБМЕЖЕНЬ

This scientific study considers the mathematical problem of optimal diversification of a portfolio of shares in the presence of market constraints. Mathematical formulation of the constructing trajectory problem of one share the market value is given in the class of ordinary first-order differential equations. The procedure for constructing a general solution of such an equation is given. Of particular practical importance is the mathematical problem of constructing an optimal portfolio structure in the presence of quantitative and qualitative market constraints. Such constraints arise at every moment of portfolio diversification, and their consideration significantly complicates the problem. The procedure for building a dynamic model of the formation of the market value of one share is based on the application of the market model of W. Sharpe and the fundamental theory by H. Markowitz. The principles of H. Markowitz theory make it possible to determine the optimal values of the portfolio's expected profitability and riskiness when applying the procedure for building an optimal portfolio of risky securities. The application of optimal management theory methods in the optimization of the stock portfolio involves an iterative procedure for determining the optimal structure. The work also considers an important applied problem of applying the theory of H. Markowitz to solve the problem of optimal diversification of a portfolio of risky investments in the presence of restrictions that are formed by the stock market at each moment of time. The presence of market restrictions significantly affects the decision-making procedure regarding optimal portfolio diversification. This scientific study presents an algorithm for optimal diversification of a portfolio of risky securities in the presence of market restrictions.