International Journal of Science, Engineering and TechnologyAuthors: Dr. Vemu Pavan Kumar
Abstract: Mathematical frameworks have become indispensable for interpreting the complexity of economic behavior and market trends, yet many traditional models fail to capture the heterogeneous, adaptive, and non‑linear nature of real‑world economies. This paper synthesizes four powerful mathematical domains that have enabled significant recent advances: behavioral game theory and equilibrium learning, agent‑based modeling with reinforcement learning, advanced time‑series forecasting using wavelet‑hidden Markov models and deep learning, and network‑theoretic approaches to systemic risk. Drawing exclusively on peer‑reviewed studies from 2025–2026, we demonstrate how these methods are applied to concrete economic problems—from green technology transitions and financial volatility prediction to macroeconomic stabilization and contagion dynamics in banking networks. Key findings include: (i) novel online optimization algorithms that solve previously intractable equilibrium problems under incomplete information; (ii) the Homo procrasticus model, which introduces effort‑based thresholds to explain inertia and default reliance; (iii) mean‑field reinforcement learning that corrects structural biases in standard agent simulations, converging to competitive equilibrium; (iv) wavelet‑enhanced multimodel frameworks that reduce stock market forecast errors by 20–40% across bull, bear, and sideways regimes; and (v) a continuous Navier‑Stokes framework for financial networks, showing that post‑COVID regulatory reforms reduced systemic contagion decay by 26%. The paper concludes with an integrated three‑layer analytical framework (micro‑behavioral, meso‑interaction, macro‑structural) that bridges individual decision rules, emergent market dynamics, and systemic risk propagation. These mathematical interpretations move economics beyond retrospective description toward predictive, prescriptive, and policy‑relevant analysis, offering directly applicable tools for risk management, policy design, and market forecasting.
DOI: http://doi.org/10.5281/zenodo.20726267
