Mathematical Problems of Applied Portfolio Analysis

  • Е.К. Ергалиев Sarsen Amanzholov East Kazakhstan State University (Ust-Kamenogorsk, Kazakhstan) Email: ergaliev79@mail.ru
  • М.Н. Мадияров Sarsen Amanzholov East Kazakhstan State University (Ust-Kamenogorsk, Kazakhstan) Email: madiyarov_mur@mail.ru
  • Н.М. Оскорбин Altai State University (Barnaul, Russia) Email: osk46@mail.ru
DOI_disc_logo https://doi.org/10.14258/izvasu(2019)1-12
Keywords: the Markowitz mean-variance analysis, substantiating optimal solutions during uncertainties, subjective utility of investment decisions, applied portfolio analysis

Abstract

  In this paper, we study mathematical models of applied portfolio analysis, methods for identifying their parameters, and numerical methods to substantiate optimal solutions. At present, the group of mathematical methods of portfolio analysis in the financial sphere is fundamentally different in two aspects. The first one is related to the choice of assets which profitability is stable, but there is a non-zero probability of losing assets. Then the purpose of the portfolio analysis is to determine the optimal set of assets at which the risks of loss are minimal. The second approach, for which the Markowitz theory is applicable, concerns selecting a set of compensatory assets. It is believed that the return on assets is a random variable, but the probability of their total losses is zero. Then the purpose of the portfolio analysis is to select a set of assets that will provide a high average return and a minimum deviation of income from this average. This paper discusses the mathematical problems of applying the Markowitz theory, which allows selecting the optimal set of compensation assets with high average returns. A set of mathematical decision-making support methods for the Markowitz theory are proposed, and the set of methods is based on the idea of forming a table of options for optimal portfolios and on using the principles of expected utility, including subjective, to choose a portfolio that corresponds to the investment preferences of decision makers.

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Author Biographies

Е.К. Ергалиев, Sarsen Amanzholov East Kazakhstan State University (Ust-Kamenogorsk, Kazakhstan)
кандидат физико-математических наук, заведующий кафедрой математики
М.Н. Мадияров, Sarsen Amanzholov East Kazakhstan State University (Ust-Kamenogorsk, Kazakhstan)
кандидат технических наук, профессор кафедры математики  
Н.М. Оскорбин, Altai State University (Barnaul, Russia)

доктор технических наук, профессор кафедры теоретической кибернетики и прикладной математики

References

Markowit s Harry M. Portfolio Selection // Journal of Finance. 19» 52. 7.№ 1.

Наумов А. А., Ходусов Н. В. Управление портфельными инвестициями. Модели и алгоритмы. Новосибирск, 2005.

Наумов А. А., Федоров А. А. Синтез эффективного портфеля проектов // Информационные технологии моделирования и управления. 200(5. № 1(26]).

Мотылль Д. Управление доходностью и ликвидностью портфеля активов банка // Рынок ценных бумаг. 1997. №14.

Оскорбин Н.М., Мадияров М.Н. Методика и инструментальным средства прикладного портфельного анализа инвестиционной стратегии // Ломоносовские чтения на Алтае: фундаментальные проблемы науки и образования - 2017 : материалы Международной конференции / отв. ред. Е.Д. Родионов. Барнаул, 2017.

Bierwag G., Kaufman G., Toevs A. Single factor duration models in a discrete general equilibrium framework // Journal of Finance. 1982. Vol. 37, №2.

Максимов А.В., Оскорбин Н.М. Многопользовательские информационные системы: основы теории и методы исследования. 2-е изд., испр. и доп. Барнаул, 2013.

Ширяев В.И. Оптимальные портфели, управление финансами и рисками. 2-е изд. М., 2009.

Бродецкий Г.Л. Системный анализ в логистике. Выбор в условиях неопределённости. М., 2010.

Данько Е.В., Оскорбин Н.М. Модель оптимизации параметров n-этапной инвестиционной экспертизы // Известия Алтайского гос. ун-та. 2014. №1/2(81).

Данько Е.В. Функция субъективной полезности инвестиционных решений в условиях информационной неопределенности и метод оценки ее параметров // Вестник Новосибирского гос. ун-та. Серия: Информационные технологии. 2015. Т. 13, вып. 3.
Published
2019-03-06
How to Cite
Ергалиев Е., Мадияров М., Оскорбин Н. Mathematical Problems of Applied Portfolio Analysis // Izvestiya of Altai State University, 2019, № 1(105). P. 75-79 DOI: 10.14258/izvasu(2019)1-12. URL: http://izvestiya.asu.ru/article/view/%282019%291-12.
Issue
No 1(105) (2019): Izvestiya of Altai State University
Section
Математика и механика

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