A Probabilistic Markov Chain Framework for
Portfolio Optimization in the Vietnamese Stock Market

Doan Thanh Son

doi:https://doi.org/10.14445/22315373/IJMTT-V72I5P105

International Journal of Mathematics Trends and Technology

Research Article | Open Access | Download PDF

Volume 72 | Issue 5 | Year 2026 | Article Id. IJMTT-V72I5P105 | DOI : https://doi.org/10.14445/22315373/IJMTT-V72I5P105

A Probabilistic Markov Chain Framework for Portfolio Optimization in the Vietnamese Stock Market

Doan Thanh Son

Received	Revised	Accepted	Published
27 Mar 2026	30 Apr 2026	15 May 2026	29 May 2026

Citation :

Doan Thanh Son, "A Probabilistic Markov Chain Framework for Portfolio Optimization in the Vietnamese Stock Market," International Journal of Mathematics Trends and Technology (IJMTT), vol. 72, no. 5, pp. 64-73, 2026. Crossref, https://doi.org/10.14445/22315373/IJMTT-V72I5P105

Abstract

The purpose of this paper is to investigate the theoretical foundations of Markov chains and to develop a model for forecasting stock price volatility based on return series. Building on this framework, the study constructs an optimal investment portfolio composed of securities with superior expected performance. The proposed model is then applied to real-world data from stocks listed on the Ho Chi Minh City Stock Exchange (HOSE). The findings of this research provide a quantitative basis for supporting investors in making more informed and effective capital allocation decisions.

Keywords

Markov chain theory, Stochastic processes, Financial markets, Forecasting stock price, Optimal investment portfolio.

References

[1] D.H. Thang, Random Processes and Stochastic Calculations, Hanoi National University Publishing House, 2006.

[2] N.D. Tien, Probability Models and their Applications. Part I: Markov Chains and Applications, Hanoi National University Publishing House, 2000.

[3] S.O.N. Agwuegbo, A.P. Adewole, and A.N. Maduegbuna, “A Random Walk Model for Stock Market Prices,” Journal of Mathematics and Statistics, vol. 6, no. 3, pp. 342-346, 2010.
[CrossRef] [Google Scholar] [Publisher Link]

[4] Kevin J. Doubleday, and Julius N. Esunge, “Application of Markov Chains to Stock Trends,” Journal of Mathematics and Statistics, vol. 7, no. 2, pp. 103-106, 2011.
[CrossRef] [Google Scholar] [Publisher Link]

[5] Grant Mcqueen, and Steven Thorley, “Are Stock Returns Predictable? A Test Using Markov Chains,” The Journal of Finance, vol. 46, no. 1, pp. 239-263, 1991.
[CrossRef] [Google Scholar] [Publisher Link]

[6] Milan Svoboda, and Ladislav Lukáš, “Application of Markov Chain Analysis to Trend Prediction of Stock Indices,” Proceedings of 30^th International Conference Mathematical Methods in Economics, pp. 848-853, 2012.
[Google Scholar] [Publisher Link]

[7] Athanasios Papoulis, and S. Unnikrishna Pillai, Probability, Random Variables and Stochastic Processes, McGraw-Hill Science, 2001.
[Google Scholar] [Publisher Link]

[8] Sean P. Meyn, and Richard L. Tweedie, Markov Chains and Stochastic Stability, Cambridge University Press, 2009.
[Google Scholar] [Publisher Link]

[9] Emanuel Parzen, Stochastic Processes, Courier Dover Publications, 2015.
[Google Scholar] [Publisher Link]

[10] John Lamperti, Stochastic Processes: A Survey of the Mathematical Theory, Springer-Verlag, 1977.
[Google Scholar] [Publisher Link]

[11] Sean P. Meyn, and Richard L. Tweedie, Markov Chains and Stochastic Stability, Cambridge University Press, 2009.
[Google Scholar] [Publisher Link]

[12] Donald L. Snyder, and Michael I. Miller, Random Point Processes in Time and Space, Springer Science & Business Media, 2012.
[Google Scholar] [Publisher Link]

[13] Ravi Bansal, Dana Kiku, and Amir Yaron, “Risks for the Long Run: Estimation with Time Aggregation,” Journal of Monetary Economics, vol. 82, pp. 52-69, 2016.
[CrossRef] [Google Scholar] [Publisher Link]

[14] Nicholas Barberis, Andrei Shleifer, and Robert Vishny, “A Model of Investor Sentiment,” Journal of Financial Economics, vol. 49, no. 3, pp. 307-343, 1998.
[CrossRef] [Google Scholar] [Publisher Link]

[15] Lars Peter Hansen, John C. Heaton, and Nan Li, “Consumption Strikes Back? Measuring Long-Run Risk,” Journal of Political Economy, vol. 116, no. 2, pp. 260-302, 2008.
[CrossRef] [Google Scholar] [Publisher Link]

[16] Lars Peter Hansen, and Ravi Jagannathan, “Implications of Security Market Data for Models of Dynamic Economies,” Journal of Political Economy, vol. 99, pp. 225-262, 1991.
[CrossRef] [Google Scholar] [Publisher Link]