Pareto Efficient Insurance with Multiple Policyholders, Multiple Insurers, and Multiple Indemnity Environments

Battle Count: 70

The paper is primarily about insurance contract design and risk sharing, not quantitative trading. However, the theoretical framework involving risk measures (VaR, CVaR-type concepts), Pareto optimality, and optimization under constraints has tangential relevance to portfolio risk management and derivative pricing. The sum-minimization characterization could inform risk allocation in multi-agent financial systems, but the direct application to trading strategies is minimal.

The theoretical framework is mathematically sophisticated but well-structured. Implementing the results would require: (1) specifying appropriate risk measures satisfying the axioms, (2) solving the sum-minimization optimization problem over feasible contract sets, (3) for bilateral implementability, applying max-flow min-cut algorithms. The mathematical proofs themselves are straightforward contradiction arguments. The main complexity lies in the optimization over function spaces (indemnity functions) rather than finite-dimensional problems.

This is a purely theoretical paper with complete mathematical proofs. All definitions, assumptions, theorems, and proofs are fully self-contained. The results can be verified by checking the mathematical arguments. No computational experiments or data are required. The paper builds on three prior works (Asimit-Boonen 2018, Asimit-Boonen-Chi-Chong 2021, Boonen-Chong-Ghossoub 2024) and combines their results.