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The efforts of researchers for analysis of the financial investment market are largely aimed at considering multi-criteria problems with a large number of criteria, studying and solving investment management problems in static and dynamic settings, building procedures for an adequate description of random processes of market price changes, developing applied numerical methods and algorithms for solving large-scale problems. These problems as tasks of management under conditions of uncertainty refer equally to the fundamental problems of the applied theory of decision-making. The researches of R. Bellman, J. Danzig, R. Merton, and G. Markowitz are aimed at establishing the fundamental foundations and studying various meaningful interpretations of financial analysis processes. Thus, in the static case, they obtained fundamental results that had a wide practical application. The property of the distribution of the optimal portfolio into risk-free and risky components for the case of the presence of a risk-free asset on the market was established, and the fundamental properties of the equilibrium market of optimal portfolios were investigated. Dynamic models of asset and liability management have found the most successful application in the field of long-term financial planning, where the need for repeated decision-making is determined by the essence of the process.

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The problem of optimal portfolio diversification is considered. Based on mathematical models of the dynamics of the market value formation of a single share and an optimal stock portfolio, the structure of the optimal portfolio is determined. Such models are built in a class of ordinary differential equations. One of the problems of optimal investing is optimizing the expected return of the stock portfolio for the desired level of risk. Another problem is the choice of the stock portfolio with the same expected return, but with a smaller risk. For this purpose, we use a set of acceptable and effective portfolios. This sequence of steps of the algorithm allows consistently solve two optimization problems. The problem of portfolio diversification consists of the problem of determining the moments of time and the necessity to perform such a diversification. In the article, we constructed an algorithm for determining these points of time, based on the solution of an optimal control problem. The application of this algorithm enables to select an optimal risk portfolio at a certain level of its expected profitability. It uses an efficient and acceptable set of investment portfolios.