A Fractal and Game-Theoretic Approach to Stock Market Analysis: An Energy-Space-Time Framework for Trading Strategy Optimization

Abstract

This study addresses the limitations of conventional stock price modeling in capturing the multi-dimensional complexities of financial markets by integrating fractal theory and game theory into a unified energy-space-time framework. Traditional approaches often fail to account for the chaotic dynamics of stock prices due to their static assumptions about market behavior, whereas this research emphasizes the interplay of capital flow dynamics (energy), structural patterns (space), and cyclical trends (time) across multiple scales. By leveraging Yang-Zhang volatility estimation and multi-fractal recursion, we construct a novel energy index to quantify multi-party capital competition and identify critical inflection points in market sentiment. Empirical analysis of benchmark stocks-such as CATL (new energy), Kweichow Moutai (consumer staples), SMIC (semiconductors), and CMB (financials)-demonstrates that sector-specific volatility profiles align with industry attributes (e.g., "high fluctuation-strong trend" in tech vs. "low volatility-slow recovery" in consumer sectors). The proposed framework further integrates deviation metrics (DVI) and risk controls (e.g., 20% stop-loss, 30% profit-taking) to generate actionable trading signals, achieving annualized returns exceeding 23% in select cases while maintaining Sharpe ratios >1.2. Philosophically, this work bridges Eastern strategic thinking (The Great Learning’s "knowing-practicing" continuum) with Western quantitative rigor, offering a paradigm for systemic risk management and long-term value creation in turbulent markets.