Кафедра мультимедійних систем

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Browsing Кафедра мультимедійних систем by Author "Yunkova, Olena"

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    Diversification of Stock Portfolio Structure under Market Restrictions
    (2023) Oletsky, Oleksiy; Kulian, Victor; Korobova, Maryna; Yunkova, Olena
    This article describes the mathematical formulation of the problems of managing a portfolio of securities on the stock market. The problem of managing a stock portfolio is considered as a mathematical problem of optimal management. Mathematical statements are formulated for problems with two fixed ends of the trajectory and for one fixed and one free end of the trajectory. For the correct formulation of optimal management problems, mathematical models are describing the dynamics of the market value formation of one share and the portfolio are applied. The corresponding models are written in the class of ordinary differential equations with parameters. 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 of 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.