Robust Optimization in Causal Models and G-Causal Normalizing Flows

Battle Count: 64

Directly addresses portfolio optimization in causal factor models with mean-variance objectives. Demonstrates interventional robustness of G-causal portfolios under distributional shifts, which is critical for out-of-sample trading performance. The G-causal Wasserstein distance framework provides theoretical guarantees for data augmentation in financial applications where distributional shifts are frequent. The paper explicitly mentions hedging, regression, and portfolio selection as motivating applications.

Requires: (1) prior knowledge or estimation of causal DAG structure, (2) custom hypercoupling flow architecture with strictly-increasing MLPs and hypernetworks, (3) careful parameterization to ensure invertibility and monotonicity, (4) training via maximum likelihood with change-of-variable formula. The architecture is modular (one coupling per node) but requires implementing custom activation functions and constrained parameter spaces. Code is provided in supplementary materials.

Source code provided in Supplementary Materials. Demo notebooks promised in a GitHub repository upon publication. All experiments use synthetic data (randomly generated linear Gaussian SCMs with Erdos-Renyi DAGs), making them fully reproducible. However, no real-world datasets are used, and the GitHub repository URL is not yet available.