Mixing-Law Uncertainty in Multivariate Normal Mean-Variance Mixtures: Semi-parametric Estimation and Robust Cumulative-Prospect Decisions

Battle Count: 55

Highly relevant for quantitative trading and portfolio management. The paper provides a rigorous framework for handling model uncertainty in multivariate return distributions, which is critical for robust portfolio allocation. The CPT-based decision framework captures realistic behavioral preferences. The distributionally robust approach avoids overfitting to a single mixing law. The 30-stock empirical application demonstrates practical applicability. The interval branch-and-bound certificate provides verifiable global optimality. However, the common-direction restriction and fixed CPT parameters limit direct implementation without adaptation.

High complexity due to: (1) EM/ECM algorithms for six parametric mixing families with determinant normalization; (2) Grid NPMLE with 45-point logarithmic grid and responsibility computation in log domain; (3) Paired circular block bootstrap with 4,000 replications; (4) CPT value computation with probability weighting and Lebesgue-Stieltjes integration; (5) Interval branch-and-bound with outward-rounding safeguards for global optimality certification; (6) Multi-dimensional numerical integration for lognormal mixing via Gauss-Hermite quadrature. Requires careful handling of Bessel functions, digamma functions, and numerical conditioning.

The paper includes comprehensive reproducibility files with Python implementations of all estimators (EM/ECM, grid NPMLE, block bootstrap, CPT calculations, interval branch-and-bound certificate). Data availability statement confirms adjusted prices, log returns, fitted-model outputs, and numerical certificates are included. Code availability statement confirms all implementations are provided. Detailed parameter tables, algorithm pseudocode, and numerical settings are fully specified.