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Progress and Convergence in Capital Market Three-Body Dynamics Experimentation
Capital Three-Body Dynamics
👤 Quantitative trading researchers, financial market analysts, technical personnel interested in three-body dynamics and strategy development
This article documents the author's progress in advancing capital market three-body dynamics experimentation in April 2026. By building a prototype in Pine Script, the author validated modeling issues for the three market state variables δ, μ, and σ, finding that defining δ using moving average deviation degenerates into a variant of μ, leading to the abandonment of this approach. The author converged on δ being understood as a deviation measure or pull-back pressure intensity, rather than a directional variable, and recommended handling it in logarithmic space. Experiments also attempted quantile central tendency and gravitational field schemes, but the latter fell short due to excessive parameters and numerical explosion issues. Key insights include the convergence of research direction: δ is the core challenge, and future work should advance gravitational field models incorporating volume anchoring, time decay, and asymmetry, while considering behavioral finance aspects like disposition effect and psychological anchoring. Gating strategy experiments showed limited effectiveness, suggesting the need for multi-cycle experiments or offline frameworks.
- ✨ δ cannot be defined using moving average deviation, as it degenerates into μ; it should be treated as a deviation measure
- ✨ Three-body dynamics should be modeled in logarithmic space to unify dimensions and interpretation
- ✨ The future direction for δ modeling is gravitational field models, incorporating volume anchoring and time decay
- ✨ Behavioral finance asymmetry (e.g., disposition effect) is key to δ modeling
- ✨ Gating strategy experiments require multi-cycle or offline frameworks, as same-cycle fine-tuning yields low returns
📅 2026-04-20 · 2,160 words · ~10 min read
Three-Body Dynamics Signal Gating Mechanism and Market State Variable Analysis
Capital Three-Body Dynamics
👤 Quantitative trading researchers, strategy developers, analysts interested in market dynamics and signal gating mechanisms
This paper first introduces a signal gating mechanism based on three-body dynamics, which determines strategy entry and exit timing by estimating market state variables δ (premium), μ (momentum), and σ (volatility) to maximize strategy returns. The author elaborates on the intuitive understanding of these three state variables: the core of δ is the psychological anchoring effect, which can be analyzed through volume distribution; the core of μ is the speed of price changes, measurable by moving averages of log returns; the core of σ is the magnitude of price changes, measurable by the standard deviation of log returns. The article also discusses criteria for judging the effectiveness of estimation methods, i.e., evaluating based on the quality of gating effects, and notes that advanced signal strategies often already include estimates of these state variables but require systematic understanding. Finally, the author suggests that after decoupling signal gating, these state variables can serve as key factors, while the signal strategy itself may only need the simplest form.
- ✨ Proposes a signal gating mechanism based on three-body dynamics, dynamically adjusting strategy entry by estimating δ, μ, and σ
- ✨ Explains in detail the intuitive understanding and estimation methods of market state variables δ, μ, and σ, emphasizing psychological anchoring, price speed, and magnitude
- ✨ Discusses criteria for judging estimation effectiveness, i.e., the improvement in strategy returns due to gating effects
- ✨ Points out that advanced signal strategies already include estimates of market state variables but require systematic understanding
- ✨ Suggests that after decoupling gating, state variables can serve as key factors, simplifying signal strategy design
📅 2026-02-10 · 1,208 words · ~6 min read
Market State Variable Modeling Scheme for Three-Body Gating
Capital Three-Body Dynamics
👤 Financial quantitative analysts, market researchers, and technical personnel interested in financial market modeling and gating mechanisms
Building on the three-body dynamics hypothesis and gating mechanism concept, this paper systematically outlines the modeling scheme for market state variables δ (premium), μ (momentum), and σ (volatility). The core innovation lies in the definition of δ: through the volume gravitational field model, nonlinear operations (Gaussian kernel functions and gradient calculations) are introduced to maintain its independence from μ and σ. μ is defined as the exponential moving average of returns to extract trend information; σ is defined as the standard deviation of returns to measure volatility amplitude; δ is based on the distribution of volume along the price axis, calculating the regression force when prices deviate from high-volume concentration areas. The article details the specific steps for calculating these three variables from candlestick sequences, including parameter settings and independence arguments, providing a new modeling framework for financial market analysis.
- ✨ δ (premium) is defined through the volume gravitational field model, introducing nonlinear operations to ensure independence from μ (momentum)
- ✨ μ is defined as the exponential moving average of returns, and σ is defined as the standard deviation of returns
- ✨ Specific steps and parameter recommendations for calculating δ, μ, and σ from candlestick sequences
- ✨ Independence arguments for the three variables (δ, μ, σ) are based on nonlinear operations and different information sources
- ✨ Kernel functions (e.g., Gaussian kernel) model psychological anchoring effects, with bandwidth adaptable to volatility
📅 2026-02-10 · 1,581 words · ~8 min read
The Three-Body Dynamics Hypothesis of Capital Markets
Capital Three-Body Dynamics
👤 Financial researchers, quantitative analysts, market participants, economics students, and professionals interested in capital market dynamics.
This paper proposes that capital markets are a three-body system composed of momentum capital (M), value capital (V), and liquidity capital (L), analogous to the three-body problem in celestial mechanics. These three types of capital interact through positive and negative feedback, generating complex dynamics such as volatility clustering, market crashes, and recoveries. The article defines the behavioral characteristics, interaction mechanisms, and feedback loops of each capital type, introduces three core variables—premium (δ), momentum (μ), and volatility (σ)—and derives eight market phases and their transition paths. The core conclusion is that when the three types of capital are balanced, markets exhibit genuine complex dynamics; long-term prediction is impossible, but short-term characteristics and statistical patterns are robust. A healthy market requires the coexistence of all three to maintain ecological balance.
- ✨ Capital markets consist of three fundamentally different types of capital—momentum capital, value capital, and liquidity capital—forming a three-body system.
- ✨ The three types of capital interact through positive and negative feedback, generating complex dynamics such as volatility clustering, market crashes, and recoveries, as well as eight market phases.
- ✨ The system's state depends on the competition between positive and negative feedback loops; long-term prediction is impossible, but short-term characteristics and statistical patterns are robust.
- ✨ A healthy market requires the coexistence and balance of all three types of capital; dominance by any one type leads to market imbalance.
- ✨ The model describes the market using three variables—premium, momentum, and volatility—and derives a return-risk-cost matrix and phase transition paths.
📅 2026-02-07 · 3,438 words · ~16 min read
Derivation of SDE Equations for Three-Body Dynamics in Capital Markets
Capital Three-Body Dynamics
👤 Financial modeling researchers, quantitative analysts, economists interested in capital market dynamics
Building on the article 'The Three-Body Dynamics Hypothesis in Capital Markets,' this paper derives a complete system of stochastic differential equations (SDEs) to describe the interactions among momentum capital (M), value capital (V), and liquidity capital (L) in capital markets. The article defines fast variables (such as log premium, momentum, volatility) and slow variables (the volumes of the three types of capital) and extracts 12 formalizable core constraints. Through a detailed analysis of the SDE equations, the article validates these constraints one by one, including positive feedback for M, negative feedback for V, directionless feedback for L, positive and negative feedback loops, payoff matrices, and crowding effects. All constraints are validated, indicating that this SDE system fully implements the qualitative mechanisms from the original article, such as volatility clustering, fat-tailed distributions, and chaotic behavior. The article also conducts phase analysis and statistical property validation, providing a foundation for subsequent numerical simulations, bifurcation analysis, and parameter calibration.
- ✨ Derived a complete SDE system describing the interactions among three types of capital
- ✨ Validated 12 core constraints, including positive/negative feedback and payoff matrices
- ✨ The system explains market characteristics such as volatility clustering and fat-tailed distributions
📅 2026-02-07 · 1,839 words · ~9 min read