Making investment decisions in the cryptocurrency market using the markowitz model and pre-trained neural networks

The article examines modern approaches to forming an optimal investment portfolio in the cryptocurrency market, including classical methods of technical analysis. Trends in the development of the global digital financial assets market are studied. Various interpretations of the concept of investment strategy are considered. Particular emphasis is placed on the Markowitz model. Its basic version and modification for crypto-futures and crypto-options are reviewed. A computer implementation of the model was developed, numerical experiments were conducted, followed by a substantive interpretation of the obtained results. An algorithm for solving the nonlinear optimization problem using pre-trained neural networks and the Pyomo framework was developed. Additionally, alternative approaches to cryptocurrency portfolio optimization are considered.

1. O razvitii tsifrovoy ekonomiki : Dekret Prezidenta Respubliki Belarus ot 21 dekabrya 2017 g. № 8 [On the development of the digital economy : Decree of the President of the Republic of Belarus of December 21, 2017 No 8]. National Legal Internet Portal of the Republic of Belarus (in Russian). Available at: https://pravo.by/document/?guid=12551&p0=Pd1700008 (accessed 21 February 2026).

2. The 2025 geography of crypto report. Chainalysis. Available at: https://www.chainalysis.com/reports/2025-geo-crypto-report/ (accessed 22 February 2026).

3. Ikhsanov I.R. Analiz investitsionnykh strategiy v kriptovalyutu [Analysis of investment strategies in cryptocurrency]. Tendentsii Razvitiya Nauki i Obrazovaniya [Trends in the Development of Science and Education]. 2022;87(3):157–161 (in Russian). doi: 10.18411/trnio-07-2022-122.

4. Vaganova O.V., Melnikova N.S., Buryak A.S., Puzankov M.N. Technical analysis as a tool for forming investment decisions in the stock market. Modern Economy Success. 2025;6:347–354 (in Russian). Available at: https:// journals.rcsi.science/2500-3747/article/view/369340 (accessed 22 February 2026).

5. Malyshenko K.A., Malyshenko V.A., Tereshchenko E.Yu. Teoriya Elliotta i eye znacheniye v razvitii fondovogo rynka [Elliott theory and its importance in the development of the stock market]. Ekonomika, Sotsiologiya i Pravo [Economics, Sociology and Law]. 2017;6:11–18 (in Russian).

6. Volobueva Е. About capabilities of application of Bloomberg system for research of the stock prices based on Elliott wave theory. Sovremennaya Matematika i Kontseptsii Innovatsionnogo Matematicheskogo Obrazovaniya: Materialy Vserossiyskoy Konferentsii [Modern Mathematics and Concepts of Innovative Mathematical Education: Proceedings of the All-Russian Conference], Moscow, May 19, 2015. Moscow; 2015. pp. 173–178 (in Russian). Available at: http://elib.fa.ru/fbook/gisin_sovremennay_matematika_sbornik.pdf (accessed 21 February 2026).

7. Chemekov R.A. Urovni Fibonachchi v treidinge [Fibonacci retracements in trading]. Nauchnomu Progressu – Tvorchestvo Molodykh: Materialy XVIII Mezhdunarodnoi Molodezhnoi Nauchnoi Konferentsii po Estestvennonauchnym i Tekhnicheskim Distsiplinam [Scientific Progress – Creativity of the Young: Proceedings of the XVIII International Youth Scientific Conference on Natural Sciences and Engineering Disciplines], Yoshkar-Ola, April 21–22, 2023. In 2 parts. Yoshkar-Ola; 2023. Part 2. pp. 391–394 (in Russian). Available at: https://science.volgatech.net/nm/Conferences/Young%20creations/sbornic2.pdf (accessed 21 February 2026).

8. Digol I.D. Effectiveness of technical analysis filtering methods: moving averages and Bollinger bands. Russian Economic Bulletin. 2023;6(3):266–273 (in Russian). Available at: https://journals.rcsi.science/2658-5286/article/view/403474/671212 (accessed 21 February 2026).

9. Karpova A.N., Dubatovskaya M.V. Technical analysis as a method of forecasting the cryptocurrency market. Osnovnye Tendentsii Ehkonomicheskogo Razvitiya Respubliki Belarus: Sbornik Dokladov II Nauchno-prakticheskogo Kruglogo Stola Prepodavatelei, Aspirantov i Studentov [Main Trends in the Economic Development of the Republic of Belarus: Collection of Reports of the II Scientific and Practical Round Table of Teachers, Graduate Students and Students], Minsk, April 15, 2020. Minsk; 2020. pp. 226–233 (in Russian). Available at: https://elib.bsu.by/handle/123456789/250997.

10. Wu J., Zhang X., Huang F., Zhou H., Chandra R. Review of deep learning models for crypto price prediction: implementation and evaluation. arXiv [Preprint]. 2024. https://doi.org/10.48550/arXiv.2405.11431.

11. Tiwari D., Bhati B.S., Nagpal B., Alturki N., Bayisenge L. Attention-augmented hybrid CNN-LSTM model for social media sentiment analysis in cryptocurrency investment decision-making. Scientific Reports. 2025;15:33201. https://doi.org/10.1038/s41598-025-18245-x.

12. Mankialevich P.V. Combined application of the recurrent neural network and technical analysis for predicting the change in the prices of the cryptate market. Forum Molodykh Uchenykh [Forum of Young Scientists]. 2019;5(33):877880 (in Russian). Available at: https://cyberleninka.ru/article/n/kombinirovannoe-primenenie-rekurrentnoy-neyronnoy-seti-i-tehnicheskogo-analiza-dlya-prognozirovaniya-izmeneniya-tsen-na-rynke (accessed 21 February 2026).

13. Fedorov G. V. Primenenie teorii Markovitsa k kriptovalyutnomu portfelyu. [Application of Markowitz's theory to a cryptocurrency portfolio]. Belgorodskii Ehkonomicheskii Vestnik [Belgorod Economic Bulletin]. 2023;2(110):91–95 (in Russian).

14. Ermakov N.S., Galkina E.A. Portfolio optimization in the era of digital financialization using cryptocurrencies. Modern Economy Success. 2021;2:164–169 (in Russian).

15. Khalyapin A.A., Streltsova T.V., Milovanov A.A., Kim S.A. Portfolio optimization in the era of digital financialization using cryptocurrencies. Estestvenno-gumanitarnye Issledovaniya [Natural Sciences and Humanities Studies]. 2025;1(57):533–538 (in Russian). Available at: https://cyberleninka.ru/article/n/optimizatsiya-portfelya-v-epohu-tsifrovoy-finansializatsii-s-ispolzovaniem-kriptovalyut (accessed 21 February 2026).