About two-criteria optimization of the stock portfolio

Authors

  • Fedir G. Garashchenko The Complex Systems Modeling Department of Computer Sciences and Cybernetics Faculty of Kyiv National Taras Shevchenko University, Kyiv, Ukraine
  • Victor R. Kulyan The Complex Systems Modeling Department of Computer Sciences and Cybernetics Faculty of Kyiv National Taras Shevchenko University, Kyiv, Ukraine https://orcid.org/0000-0002-6320-4719
  • Olena O. Iunkova The Economic and Mathematical Modeling Department of Information Systems and Technology Faculty of Kyiv National Vadim Getman University, Kyiv, Ukraine

DOI:

https://doi.org/10.20535/SRIT.2308-8893.2017.3.02

Keywords:

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

Abstract

This scientific research is devoted to developing the new and known application of mathematical modeling for solving the problem of optimal investment in risky securities. The objectives for new problems are formulated and trajectory modeling methods are constructed for the market value dynamics of a single share and the whole stock portfolio. While solving the problem of modeling the optimal trajectory of the portfolio of shares, methods of optimal system control were utilized in which the fractions of different kinds of shares in the portfolio were used as the control parameters. The problems for the optimal control dynamics of the investment portfolio are formulated for quality criteria, one of which uses "a soft path" and the second - a deviation from the estimated trajectory of the terminal value. Thus, the first part of the work is devoted to solving the problem of constructing the optimal expected market value of the portfolio shares. The second part deals with the problem of optimizing the portfolio based on risk. To solve it, the admissible and effective sets of investment portfolios are applied. The algorithm for solving the problem allows to dynamically take into account the instrumental market constraints that are formulated in the mathematical formulation of the problem.

Author Biographies

Fedir G. Garashchenko, The Complex Systems Modeling Department of Computer Sciences and Cybernetics Faculty of Kyiv National Taras Shevchenko University, Kyiv

Fedir Garashchenko,

professor, Doctor of Engineering Sciences, the Head of the Complex Systems Modeling Department of Computer Sciences and Cybernetics Faculty of Kyiv National Taras Shevchenko University, Kyiv, Ukraine.

Victor R. Kulyan, The Complex Systems Modeling Department of Computer Sciences and Cybernetics Faculty of Kyiv National Taras Shevchenko University, Kyiv

Victor Kulyan,

an associate professor, Ph.D., a lecturer at the Complex Systems Modeling Department of Computer Sciences and Cybernetics Faculty of Kyiv National Taras Shevchenko University, Kyiv, Ukraine.

Olena O. Iunkova, The Economic and Mathematical Modeling Department of Information Systems and Technology Faculty of Kyiv National Vadim Getman University, Kyiv

Olena Iunkova,

an associate professor, Ph.D., a lecturer at the Economic and Mathematical Modeling Department of Information Systems and Technology Faculty of Kyiv National Vadim Getman University, Kyiv, Ukraine.

References

Sharp U. Investitsii / Uil'jam F. Sharp, Gordon Dzh. Aleksander, Dzheffri V. Bejli. — M.: Infra-M, 1999. — S.1027.

Garaschenko F.G. Kachestvennyj analiz matematicheskih modelej investitsionnogo menedzhmenta / F.G. Garaschenko, V.R. Kuljan, V.V. Rutitskaja // Kibernetika i vychislitel'naja tehnika. — 2005. — № 148. — S. 3–10.

Fedir G. Garashchenko Modelling and Analysis of Investment Trends / Fedir G. Garashchenko, Viktor R. Kulian, Vladislava V. Rutitskaya // Journal of Automation and Information. — New York: Connecticut, 2011. — 43, Issue 12. — P. 48–58.

Yuri Zaychenko Direct and dual problem of investment portfolio optimization under uncertainty / Yuri Zaychenko, Inna Sydoruk // International Journal “Information Technologies & Knowledge”. — 2014. — 8, N 3. — P. 225–242.

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Published

2017-09-29

Issue

No. 3 (2017)

Section

Progressive information technologies, high-efficiency computer systems

License

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