Robust distortion risk metrics and portfolio optimization

Battle Count: 79

Highly relevant for quantitative risk management and portfolio construction. The paper provides explicit worst-case bounds for VaR, ES, GlueVaR, and variability measures under realistic uncertainty sets (mean-variance + Wasserstein + unimodality). The robust portfolio optimization framework directly applies to position sizing and risk budgeting. The Basel regulatory context (ES vs VaR discrepancy) is particularly relevant for institutional trading desks. However, the paper is primarily theoretical and requires significant mathematical expertise to implement in practice.

High complexity due to: (1) computing concave envelopes of general distortion functions, (2) solving for the optimal lambda parameter via Wasserstein distance constraint, (3) L2-projection onto concave-convex function spaces for unimodal case, (4) numerical optimization for step-function approximations (Proposition 3 with 3n or 3n+3 parameters), (5) handling non-convexity when inflection point is unknown. The theoretical framework is elegant but translating to production code requires careful numerical implementation.

The paper provides complete mathematical proofs in the appendix and numerical examples using MATLAB. However, the theoretical results require significant mathematical expertise to implement. The numerical examples are limited to a 2-asset case. No code repository is provided. The algorithms for computing projections (Propositions 3-4) are described but not fully implemented in code.