Paper: arXiv 2604.24546

Authors: Christopher Blier-Wong, Jean-Gabriel Lauzier

Abstract

Regulatory and contractual constraints on individual exposures are standard in insurance and reinsurance markets, but a poorly designed constraint can distort the economic incentives of risk-averse agents. In the unconstrained problem, the classical comonotonic improvement theorem guarantees Pareto-optimal allocations that are nondecreasing in the aggregate loss. A constraint that is not stable under risk reduction can destroy this property. We show by example that Value-at-Risk caps lead to optimal allocations that are non-comonotonic in the aggregate loss. We identify componentwise convex-order solidity as a sufficient condition on the feasible set that restores the comonotonic improvement under constraints. If replacing any agent’s allocation by a less risky one preserves feasibility, then every feasible allocation admits a feasible comonotonic improvement for all convex-order-consistent preferences. This criterion covers many constraints typical in risk management, but excludes Value-at-Risk caps and idiosyncratic deductibles. We illustrate the implications of our main result in a mean-variance risk-sharing application.

Complexity vs Empirical Score

  • Math Complexity: 8.0/10
  • Empirical Rigor: 2.0/10
  • Quadrant: Lab Rats — theoretically deep, empirically untested

Why this score: The paper provides a rigorous mathematical framework and theoretical proof for comonotonic improvements under risk-sharing constraints, demonstrating high mathematical complexity. However, it is purely theoretical with no empirical backtesting or historical dataset validation, placing it in the ‘Lab Rats’ quadrant.

Research Flowchart

  flowchart TD
    A[Research Goal: Restore Comonotonic Optimality Under Feasibility Constraints] --> B[Inputs: Aggregate Risk Exposures & Constraints]
    B --> C[Counterexample Analysis: Value-at-Risk Caps Fail Comonotonicity]
    C --> D[Theoretical Development: Proving Componentwise Convex-Order Solidity]
    D --> E[Application: Testing Constraints in Mean-Variance Risk-Sharing]
    E --> F[Key Outcome: Solidity Condition Guarantees Feasible Comonotonic Improvements]

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1 of 45 cited works are in the corpus; resolved via arXiv source bundles, Semantic Scholar and OpenAlex. Corpus-wide: 2518 linked papers.