Bayesian Distributionally Robust Merton Problem with Nonlinear Wasserstein Projections

Battle Count: 56

Directly addresses continuous-time portfolio selection (Merton problem) with distributional robustness. Provides a principled framework for frequent rebalancing while handling drift uncertainty. Demonstrates improved performance over myopic DRO-Markowitz and reduced pessimism vs. DRC. Uses real S&P 500 data with daily trading. The Wasserstein projection-based radius calibration is directly applicable to practical portfolio construction. The Bayesian filtering structure enables adaptive portfolio weights based on observed prices.

Requires implementing: (1) Bayesian filtering for drift estimation, (2) Karatzas-Zhao closed-form portfolio weights, (3) Wasserstein gradient computation for worst-case prior perturbation, (4) Nonlinear Wasserstein projection for radius calibration via Monte Carlo, (5) Ledoit-Wolf covariance estimation, (6) Rolling window data processing. The 7-step algorithm is well-specified but involves multiple numerical components (Gaussian integrals, Monte Carlo estimation, optimization over probability measures). Theoretical understanding of Sion minimax theorem and optimal transport is needed.

The paper provides detailed algorithms (7-step recipe in Section 4), explicit formulas for worst-case priors, and synthetic data generation procedures. Real data comes from WRDS (S&P 500 constituents 2017-2024), which requires subscription. No code repository is mentioned. Theoretical proofs are complete but complex. Key parameters (B0, dt, kappa distributions) are specified for synthetic experiments.