Optimal stock portfolio diversification under market constraints

Authors

DOI:

https://doi.org/10.20535/SRIT.2308-8893.2020.1.08

Keywords:

mathematical model, acceptable set, efficient set, diversification of the investment portfolio

Abstract

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.

Author Biographies

Victor R. Kulian, Taras Shevchenko National University of Kyiv, Kyiv

Victor Kulian,

Ph.D., an associate professor at the Department of Complex Systems Modelling of Faculty of Computer Science and Cybernetics of Taras Shevchenko National University of Kyiv, Kyiv, Ukraine.

M. V. Korobova, Taras Shevchenko National University of Kyiv, Kyiv

Marina Korobova,

Ph.D., an associate professor at the Department of Complex Systems Modelling of Faculty of Computer Science and Cybernetics of Taras Shevchenko National University of Kyiv, Kyiv, Ukraine.

Olena O. Yunkova, Kyiv National Economic University named after Vadym Hetman, Kyiv

Olena Yunkova,

Ph.D., an associate professor at the Economic and Mathematical Modelling Department of Kyiv National Economic University named after Vadym Hetman, Kyiv, Ukraine.

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Published

2020-06-23

Issue

Section

Methods of optimization, optimum control and theory of games