A NUMERICAL MULTI-AGENT MODEL FOR AN ADAPTIVE SELF-ORGANIZING TRADING SYSTEM

The purpose of the study is to develop an adaptive mathematical model for forecasting financial markets based on the Financial instruments exhibit the greatest sensitivity to trading volumes (β=0.67), which corresponds with UCRME data [9], where the importance of volume indicators for forecasting financial market dynamics is emphasised.principles of self-organisation. This study presents a mathematical model of a self-organising trading system adapted to the economic conditions of the Republic of Uzbekistan. The study employs multi-agent modelling techniques, the theory of nonlinear dynamics, and spectral analysis of time series to construct an adaptive decisionmaking mechanism for trading under high volatility in emerging markets. The mathematical model is based on a system of stochastic differential equations that describe the dynamics of price formation, accounting for the interaction of multiple agents. A modified fourth-order Runge-Kutta method was applied to solve the system, achieving a rootmean-square error of 0.0124 for one-day forecasting, which outperforms conventional approaches by 15.6%. The developed algorithm for identifying market regimes, based on self-organising Kohonen maps, demonstrated an 87.6% accuracy in classifying six identified clusters of market states, enabling efficient adaptation of the system’s parameters to changing market conditions and substantially reducing forecasting errors, with the magnitude of improvement varying across market regimes. Trading strategies based on the proposed model achieved an annual return of 37.2% with a Sharpe ratio of 1.86, significantly outperforming both passive investment strategies and conventional algorithmic trading methods. The advantage of the proposed approach is particularly evident under the conditions of high volatility typical of emerging markets, where the forecasting accuracy of price movement direction reaches 72.8% for a one-day horizon. The practical value of the findings lies in the development of an adaptive trading system capable of improving the efficiency of exchange trading and the liquidity of the markets of Uzbekistan and other emerging economies.

1. Xiang, L., Tan, Y., Shen, G., and Jin, X. Applications of Multi-Agent Systems from the Perspective of Construction Management: A Literature Review. Engineering, Construction and Architectural Management, 29 (9), 3288–3310 (2022). https://doi.org/10.1108/ECAM-01-2021-0038

2. Tang, G., Tian, R., and Wu, B. An Overview of Clustering Methods in the Financial World. In: Proceedings of the 2022 7th International Conference on Financial Innovation and Economic Development (ICFIED 2022) (Dordrecht: Atlantis Press, 2022), pp. 524–529. https://doi.org/10.2991/aebmr.k.220307.084

3. Cremasco, H., Galvan, D., Angilelli, K.G., Borsato, D., and Oliveira, A.G.D. Influence of Film Coefficient During Multicomponent Diffusion–KCl/NaCl in Biosolid for Static and Agitated System Using 3D Computational Simulation. Food Science and Technology, 39, 173–181 (2019). https://doi.org/10.1590/fst.40917

4. Rahmani, D., Fay, D., and Brodzki, J. A Self-Organising Eigenspace Map for Time Series Clustering. arXiv (2019). https://doi.org/10.48550/arXiv.1905.05540

5. Fayziev, R., Kurbonov, F., and Mirzoev, A. A Mathematical Model to Attract Investments for Power Supply in the Republic of Uzbekistan. E3S Web of Conferences, 541, 02002 (2024). https://doi.org/10.1051/e3sconf/202454102002

6. Sattorov, S., Kotenko, A., Saidivaliev, S., Barotov, J., and Rustamov, N. Development of the Fundamentals for Organizing the Transportation of Local Goods on the Railways of the Republic of Uzbekistan. E3S Web of Conferences, 460, 06015 (2023). https://doi.org/10.1051/e3sconf/202346006015

7. Makhmudov, S.A. Forecasting Banking System Liquidity Using Payment System Data in Uzbekistan (Geneva: Graduate Institute of International and Development Studies, 2025). https://doi.org/10.71609/iheid59zs-d319

8. Mukhamedova, Z., and Ergasheva, Z. Economic and Mathematical Model of Container Block-Trains. AIP Conference Proceedings, 2624, 040005 (2023). https://doi.org/10.1063/5.0132553

9. Uzbek Commodity and Raw Materials Exchange. (2024). URL: https://uzex.uz/Home/Analytics

10. ISO/IEC 19795-1:2021. Information Technology – Biometric Performance Testing and Reporting – Part 1: Principles and Framework (2021). URL: https://www.iso.org/standard/73515.html

11. Kloeden, P.E., and Platen, E. Numerical Solution of Stochastic Differential Equations (Heidelberg: Springer Berlin, 1992). https://doi.org/10.1007/978-3-662-12616-5

12. Hagenau, M., Liebmann, M., and Neumann, D. Automated News Reading: Stock Price Prediction Based on Financial News Using Context-Capturing Features. Decision Support Systems, 55 (3), 685–697 (2013). https://doi.org/10.1016/j.dss.2013.02.006

13. Guilbaud, F., and Pham, H. Optimal High-Frequency Trading in a Pro Rata Microstructure with Predictive Information. Mathematical Finance, 25 (3), 545–575 (2015). https://doi.org/10.1111/mafi.2015.25.issue-3

14. Wang, Y. Mathematical Problems in Algorithmic Trading and Financial Regulation (2020). https:// doi.org/10.2139/ssrn.3593824

15. Feng, F., He, X., Wang, X., Luo, C., Liu, Y., and Chua, T.S. Temporal Relational Ranking for Stock Prediction. ACM Transactions on Information Systems, 37 (2), 27 (2019). https://doi.org/10.1145/3309547

16. Pei, D., Luo, C., and Liu, X. Financial Trading Decisions Based on Deep Fuzzy Self-Organizing Map. Applied Soft Computing, 134, 109972 (2023). https://doi.org/10.1016/j.asoc.2022.109972

17. Aus dem Moore, N., Großkurth, P., and Themann, M. Multinational Corporations and the EU Emissions Trading System: The Specter of Asset Erosion and Creeping Deindustrialization. Journal of Environmental Economics and Management, 94, 1–26 (2019). https://doi.org/10.1016/j.jeem.2018.11.003

18. Cosbey, A., Droege, S., Fischer, C., and Munnings, C. Developing Guidance for Implementing Border Carbon Adjustments: Lessons, Cautions, and Research Needs from the Literature. Review of Environmental Economics and Policy, 13 (1), 3–22 (2019). https://doi.org/10.1093/reep/rey020

19. Jarusek, R., Kaczmarek, K., and Sevastjanov, P. A Multi-Model Approach to the Development of Algorithmic Trading Systems for the Forex Market. Expert Systems with Applications, 229, 120438 (2023). https://doi.org/10.1016/j.eswa.2023.120438

20. Tran, M., Pham-Hi, D., and Bui, M. Optimizing Automated Trading Systems with Deep Reinforcement Learning. Algorithms, 16 (1), 23 (2023). https://doi.org/10.3390/a16010023

21. Scott, M., and Pitt, J. Interdependent Self-Organizing Mechanisms for Cooperative Survival. Artificial Life, 29 (2), 198–234 (2023). https://doi.org/10.1162/artl_a_00403

22. Vaccaro, A., Iuliano, S., Galdi, V., Calderaro, V., and Graber, G. Achieving Consensus in SelfOrganizing Electric Vehicles for Implementing V2G-Based Ancillary Services. IEEE Access, 12, 137222– 137236 (2024). https://doi.org/10.1109/ACCESS.2024.3465230

23. Khodoomi, M., and Sahebi, H. Robust Optimization and Pricing of Peer-To-Peer Energy Trading Considering Battery Storage. Computers & Industrial Engineering, 179, 109210 (2023). https://doi.org/10.1016/j.cie.2023.109210

24. Javadi, M.S., Gough, M., Nezhad, A.E., Santos, S.F., Shafie-khah, M., and Catalao, J.P. Pool Trading Model Within a Local Energy Community Considering Flexible Loads, Photovoltaic Generation and Energy Storage Systems. Sustainable Cities and Society, 79, 103747 (2022). https://doi.org/10.1016/j.scs.2022.103747

25. Song, M., Zheng, H., and Shen, Z. Whether the Carbon Emissions Trading System Improves Energy Efficiency – Empirical Testing Based on China’s Provincial Panel Data. Energy, 275, 127465 (2023). https://doi.org/10.1016/j.energy.2023.127465

26. Sato, M., Rafaty, R., Calel, R., and Grubb, M. Allocation, Allocation, Allocation! The Political Economy of the Development of the European Union Emissions Trading System. WIREs Climate Change, 13 (5), e796 (2022). https://doi.org/10.1002/wcc.796

27. Yudin, P.V., and Grinyak, V.M. Neuro-Fuzzy Model of Reliability Evaluation of the Sales Planning. In: Proceedings of the 2020 International Multi-Conference on Industrial Engineering and Modern Technologies (FarEastCon) (New York: IEEE, 2020), pp. 1–4. https://doi.org/10.1109/FarEastCon50210.2020.9271075