Paper: arXiv 2509.08183

Authors: Crystal Rust

Abstract

We introduce a new risk modeling framework where chaotic attractors shape the geometry of Bayesian inference. By combining heavy-tailed priors with Lorenz and Rossler dynamics, the models naturally generate volatility clustering, fat tails, and extreme events. We compare two complementary approaches: Model A, which emphasizes geometric stability, and Model B, which highlights rare bursts using Fibonacci diagnostics. Together, they provide a dual perspective for systemic risk analysis, linking Black Swan theory to practical tools for stress testing and volatility monitoring.

Complexity vs Empirical Score

  • Math Complexity: 8.0/10
  • Empirical Rigor: 3.0/10
  • Quadrant: Lab Rats — theoretically deep, empirically untested

Why this score: The paper is dense with advanced mathematics, including chaotic dynamics, Bayesian inference, and complex geometric diagnostics, while the empirical evidence is limited to simulated data without real-world backtests or implementation details.

Research Flowchart

  flowchart TD
  A["Research Goal: Model Black Swan Events"] --> B{"Data: Historical Volatility &<br>Extreme Event Distributions"}
  B --> C["Methodology: Chaotic Bayesian Inference"]
  C --> D["Model A: Lorenz Dynamics<br>Geometric Stability"]
  C --> E["Model B: Rossler Dynamics<br>Fibonacci Rare Bursts"]
  D --> F["Computational Process:<br>MCMC Sampling<br>Strange Attractors"]
  E --> F
  F --> G["Outcomes: Volatility Clustering<br>Heavy Tails & Stress Testing"]