Research on applying Riemannian geometry to financial time series analysis. Focus on manifold-aware learning algorithms for market volatility prediction and portfolio optimization.
Overview
This work explores the application of differential geometry to machine learning in financial markets. Traditional Euclidean methods often fail to capture the intrinsic structure of financial data, which naturally lies on curved manifolds.
Contributions
- Novel Riemannian optimization algorithms for portfolio selection
- Manifold-aware neural networks for volatility forecasting
- Theoretical analysis of convergence properties on curved spaces
- Empirical validation on real market data
Results
Results demonstrate significant improvements in prediction accuracy and risk-adjusted returns compared to conventional approaches. The framework has been implemented using JAX for efficient automatic differentiation on manifolds.