Comonotonic improvement under feasibility constraints
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arXiv
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| Format: | Preprint |
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2026
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| _version_ | 1866910170047578112 |
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| author | Blier-Wong, Christopher Lauzier, Jean-Gabriel |
| author_facet | Blier-Wong, Christopher Lauzier, Jean-Gabriel |
| contents | 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2604_24546 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Comonotonic improvement under feasibility constraints Blier-Wong, Christopher Lauzier, Jean-Gabriel Theoretical Economics Mathematical Finance 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. |
| title | Comonotonic improvement under feasibility constraints |
| topic | Theoretical Economics Mathematical Finance |
| url | https://arxiv.org/abs/2604.24546 |