Endogenous Reinsurance Pricing in Large Competitive Insurance Markets: Finite-Player and Mean Field Analysis

Battle Count: 85

The paper is primarily about insurance and reinsurance market equilibrium, not about trading strategies or financial market microstructure. While it involves investment decisions in risky assets and common/idiosyncratic financial-market noise, the core contribution is in reinsurance pricing and insurer retention behavior. The mean-variance framework and exponential utility are standard in quantitative finance, but the application domain is actuarial/insurance rather than trading. The game-theoretic and mean field techniques could be tangentially relevant to market-making or competitive trading models, but the paper does not address trading directly.

The theoretical framework involves Stackelberg-Nash games, mean field games, fixed-point equations, and threshold continuation procedures. Implementing the finite-player threshold continuation procedure requires sorting 2N-1 thresholds and solving linear/quadratic optimization on each interval (O(N²) complexity). The mean field version requires solving integral fixed-point equations numerically. The proofs are mathematically sophisticated (contraction mapping, Gaussian mean-variance reduction, weak convergence arguments). However, the final computational procedure is well-structured and algorithmic. No code is provided, and implementing the full framework from scratch would require significant expertise in stochastic control and game theory.

The paper is fully theoretical with complete mathematical proofs in appendices. Numerical illustrations (Figures 1-6) use specified parameter values (a_i, gamma_i, theta_i, v_{i,0}, v_i, gamma_L) that allow replication of the plots. However, no code repository or software implementation is provided. The threshold continuation procedure is described algorithmically but not implemented in code. The mean field explicit characterization under theta-only heterogeneity (Appendix D) provides closed-form expressions that can be independently verified.