Universal Value-at-Risk superadditivity

Battle Count: 105

The paper is highly relevant to risk management and portfolio construction but less directly applicable to quantitative trading strategies. Key implications: (1) For portfolios satisfying WUVS, diversification is never beneficial - optimal allocation concentrates on a single asset, which contradicts standard portfolio theory assumptions; (2) All distortion risk measures (including VaR, ES) become superadditive, affecting risk budgeting; (3) Results apply to extremely heavy-tailed/infinite-mean losses relevant to tail-risk hedging and catastrophic event modeling. The theoretical nature limits direct implementation in trading systems.

The paper is purely theoretical with advanced mathematical machinery including stochastic orders, convex analysis, distributional mixtures, and extreme value theory. Implementing the theoretical results would require: (1) verifying UVS/WUVS conditions for specific distribution families, (2) checking convex transformation preservation properties, (3) handling infinite-mean distributions numerically, (4) computing VaR for sums of heavy-tailed random variables. The mathematical proofs are complex but the conceptual framework (stochastic dominance representation) is relatively straightforward to apply.

The paper is purely theoretical with complete mathematical proofs. All results are self-contained with formal definitions, lemmas, theorems, and propositions. Figures are generated via simulation (e.g., Pareto and St. Petersburg lottery examples). No external data or code repository is mentioned, but the mathematical framework is fully reproducible from the proofs provided.