relativistic_optimizer.hpp File Reference

Relativistic Portfolio Optimization on the Financial Manifold. More...

#include "portfolio_manifold.hpp"
#include <Eigen/Dense>
#include <optional>
#include <vector>

Go to the source code of this file.

Classes
struct	srfm::portfolio::OptimizerConfig
	Tuning parameters for the relativistic portfolio optimizer. More...
struct	srfm::portfolio::OptimizationResult
	Result of a single portfolio optimization run. More...
class	srfm::portfolio::RelativisticPortfolio

Namespaces
namespace	srfm
namespace	srfm::portfolio

Detailed Description

Relativistic Portfolio Optimization on the Financial Manifold.

Module: Relativistic Portfolio Optimizer

Responsibility

Formulate the Markowitz mean-variance portfolio optimization problem as a geodesic problem on the N-asset financial manifold, replacing the Euclidean variance risk measure with the geodesic distance in the Lorentzian manifold.

Key Idea

Classical Markowitz minimises w^T Σ w subject to w^T μ = r_target, Σw = 1. Here we replace the quadratic risk measure w^T Σ w with the spacetime geodesic distance between the current portfolio state and the target return state on the financial manifold. This penalises large displacements in the "causal" (TIMELIKE) direction more heavily than classical variance.

Additionally, expected returns are corrected by the Lorentz factor γ(β): μ_rel_i = γ(β_i) · μ_i where β_i is the normalised price velocity for asset i, computed from its AssetEvent. High-velocity (noisy) assets are down-weighted; causal (low-β) assets retain full expected return.

Optimization Problem

minimise d_geo(w, w_0)² (geodesic risk measure) subject to w^T μ_rel ≥ r_target (relativistic return constraint) Σ_i w_i = 1 (full investment) w_i ≥ 0 (long-only)

Solved via projected gradient descent on the simplex.

Guarantees

• Returns nullopt rather than throwing on degenerate inputs.
• No raw pointers; Eigen3 owns all matrix storage.
• All iterative algorithms are bounded (max_iterations parameter).

Dependencies

• Eigen3
• include/portfolio_manifold.hpp (AssetEvent, MinkowskiCovariance)
• srfm/constants.hpp

Definition in file relativistic_optimizer.hpp.