# Кафедра мультимедійних систем

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### Browsing Кафедра мультимедійних систем by Author "Oletsky, Oleksiy"

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Item Diversification of Stock Portfolio Structure under Market Restrictions(2023) Oletsky, Oleksiy; Kulian, Victor; Korobova, Maryna; Yunkova, OlenaThis 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.Item A Model of Information Influences on the Base of Rectangular Stochastic Matrices in Chains of Reasoning with Possible Contradictions(2021) Oletsky, OleksiyA way of implementing the model "state-probability of choice", which describes probabilities of making a choice between certain alternatives, into chains of uncertain reasoning has been suggested. That means associating a special matrix, called rectangular stochastic matrix, with each node of the reasoning chain, whereas a node corresponds either to a given fact or to a rule of inference, maybe uncertain. A binary case, when a resolution has to be either rejected or accepted, has been regarded. A situation of a dynamic equilibrium, which means that none of these alternatives has advantage over the other, and possible ways of how agents of influence can break such a situation, have been demonstrated. Some ways of resolving conflicts between contradictory sources of evidence have been suggested.Item Some Ways of Enhancing Recommendations Aimed at Improving Positions of Alternatives on the Base of AHP(2023) Oletsky, Oleksiy; Tryhub, Oleksander; Franchuk, Ivan; Dosyn, DmytroSuggestions on enhancing the approach to elaborating recommendations about improving alternatives, which are to be chosen, on the base of the Analytic Hierarchy Process, and those on supplementing the recommender system based on this approach, are made in the paper. These suggestions are aimed both at implementing various options for recommendations about actual betterment of alternatives and at justifying possible satisfactory choices. Within the latter, possibilities related to fixing inconsistencies in the initial pairwise comparison matrices are discussed and illustrated.