Theoretical and Methodological Framework of the CBD Formula_Monte Carlos

Cadre Théorique et Méthodologique de la Formule CBD_Monte Carlos.pdf

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Theoretical and Methodological Framework of the CBD Formula_Monte Carlos.pdf

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The CBD formula models collective dynamics (crowds, markets, AI) using a nonlinear deterministic framework, with variables such as thresholds (S, R), memory (M), and energy (V).

Monte Carlo simulations (10,000 iterations) show an asymmetric distribution capturing realistic instabilities without pure randomness.

Sensitivity analysis (OAT and Sobol) identifies M and V as key amplifiers, with moderate interactions confirming robustness.

Empirical and logarithmic validation reveals heavy tails and asymmetries, consistent with real-world data (e.g., S&P 500).

Out-of-sample predictive validation demonstrates medium-term forecasting capabilities, strengthening the model's applicability.