Comonotonic improvement under feasibility constraints

Battle Count: 82

The paper is primarily relevant to insurance, reinsurance, and regulatory capital allocation rather than quantitative trading. However, the mean-variance risk-sharing framework and the analysis of VaR vs ES constraints have indirect relevance to portfolio risk management and capital allocation in trading desks. The Basel III FRTB discussion (ES_0.975 at trading-desk level) connects to market risk management in trading. The theoretical results on when comonotonicity breaks under constraints could inform understanding of counterparty risk allocation in structured products.

The theoretical framework requires deep understanding of convex order theory, inf-convolution of risk measures, and optimization under constraints. Implementing the constrained mean-variance solution (Theorem 4) requires solving statewise quadratic programs with box constraints and determining the shadow price function via fixed-point equations. The truncated-affine form is computationally tractable, but general constrained risk-sharing problems require numerical optimization. The counterexample constructions (Examples 1-3) are analytically specified but verifying non-comonotonicity in continuous settings requires careful measure-theoretic reasoning.

The paper is purely theoretical with complete mathematical proofs. All theorems, definitions, and examples are self-contained with explicit computations. However, there is no accompanying code, numerical implementation, or dataset. Reproduction requires verifying proofs and replicating the analytical examples (Examples 1-3, mean-variance applications). The mathematical framework is fully specified but implementation would require custom numerical optimization for the constrained mean-variance problem.