Our Approach

We model financial markets as dynamical systems where statistical properties evolve according to Hamiltonian mechanics in phase space

Physics-Based Market Analysis

Traditional approaches attempt to predict market movements directly from historical patterns. We take a fundamentally different approach by modeling how the statistical properties of markets evolve over time using principles from statistical mechanics.

Our theoretical framework treats market descriptors as position coordinates in a higher-dimensional phase space, with their rates of change serving as conjugate momentum variables. This allows us to apply Hamilton's equations of motion to predict future market states.

By focusing on the evolution of statistical properties rather than price movements directly, we gain insights into market behaviour that are invisible to conventional Kolmogorovian analytical approaches.

Hamiltonian Evolution

∂q/∂t = ∂H/∂p
∂p/∂t = -∂H/∂q

Market parameters q and their conjugate momenta p evolve according to Hamilton's equations, conserving phase space volume

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Energy Conservation

System energy (kinetic + potential) serves as a measure of market volatility and predictability, following conservation principles from classical mechanics and thermodynamics.

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Regime Classification

Market states are characterized through proprietary spectral analysis and phase-space classification methodologies that identify distinct behavioural regimes across different market energy conditions.

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Bayesian Sampling

Advanced Riemannian Manifold Hamiltonian Monte Carlo methods generate robust posterior distributions, enabling confident statistical inference about future market evolution.

Research Foundation

Our methodology combines rigorous statistical mechanics with advanced computational methods

  • Hamiltonian Dynamics Uses Hamilton's equations to predict how market statistical parameters evolve, providing forward-looking insights rather than reactive analysis.
  • Phase Space Analysis Models market parameters as coordinates in phase space with associated momenta, enabling trajectory prediction and dynamic stability analysis.
  • Distribution Analysis Employs a comprehensive family of probability distributions to characterize different market regimes and tail behaviours.
  • RMHMC Sampling Advanced Riemannian Manifold Hamiltonian Monte Carlo methods with multiple independent chains ensure robust posterior sampling and convergence diagnostics.
  • Risk Assessment and Quantification Incorporates tail risk assessment through extreme value theory and robust thermodynamic and statistical measures for comprehensive risk evaluation.
  • Multi-Dimensional Analysis Analyzes market behaviour through phase-space trajectories and their evolution patterns rather than price movements and regression analysis.

Core Principle

"The fundamental object of study is not the market itself, but the evolution of its statistical properties through a phase space governed by the laws of physics."