Nash Peer-to-Peer Insurance Bargaining under Price Fairness and Coalitional Stability

Battle Count: 65

The paper is primarily about insurance contracting and risk-sharing mechanism design, not quantitative trading. However, it has tangential relevance to: (1) risk management frameworks that could inform portfolio hedging strategies; (2) game-theoretic bargaining models applicable to over-the-counter derivative pricing; (3) the concept of disagreement points and outside options relevant to bilateral negotiation in trading; (4) coalitional stability concepts applicable to consortium-based risk transfer. The mathematical tools (convex optimization, KKT conditions, Nash bargaining) are broadly applicable but the specific domain is insurance, not trading.

High complexity due to: (1) solving nonlinear first-order KKT systems for the general heterogeneous case (Theorem 3.8); (2) verifying coalitional stability conditions across all 2^n - 2 subgroups (though sufficient conditions reduce this); (3) computing moment generating functions and their derivatives for exponential utility cases; (4) handling three distinct reinsurance regimes with boundary conditions; (5) numerical optimization over the simplex with price-fairness constraints. The exponential utility homogeneous case (Proposition 3.17) is more tractable with closed-form characterizations. Implementation requires careful handling of convex optimization, root-finding for premium bounds, and numerical integration for expected utilities.

The paper provides complete mathematical proofs in the appendix (Appendices A-O), explicit numerical parameters (Table 1, Table 6), and well-defined model specifications. All distributions (Gamma), utility functions (exponential), and parameter values are fully specified. However, no code or computational scripts are provided. The numerical analysis is reproducible given the stated parameters and the characterization theorems (Theorem 3.8, Proposition 3.13, Proposition 3.17).