Pareto and Bowley Reinsurance Games in Peer-to-Peer Insurance

Battle Count: 50

The paper is primarily focused on insurance and reinsurance contract design rather than quantitative trading. However, the mean-variance optimization framework, game-theoretic modeling of strategic interactions, and risk-sharing mechanisms have conceptual parallels with portfolio optimization and market microstructure. The cooperative game theory and core analysis could inform understanding of counterparty risk in trading networks. The relevance is indirect and limited to shared mathematical tools rather than direct trading applications.

The analytical solutions involve matrix operations (inversion of positive definite matrices, diagonal dominance checks) and solving systems of linear equations. The cooperative game requires computing coalition values for all subsets, which is exponential in the number of members. The closed-form solutions are elegant but require careful handling of conditions (e.g., Condition 7, 19, 22, 24) to ensure feasibility. Numerical implementation would require standard linear algebra libraries but the game-theoretic verification (core membership) adds complexity.

The paper provides fully closed-form analytical solutions for both Pareto and Bowley designs, with explicit matrix expressions. Numerical examples include specific parameter values (3-member case with given mu, Sigma, gamma vectors). All proofs are provided in appendices. However, no code or computational scripts are mentioned as available. The mathematical derivations are self-contained and reproducible from the stated assumptions.