Equilibrium analysis in a multi-agent reinsurance chain

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This paper is primarily focused on insurance and reinsurance market equilibrium rather than quantitative trading. While it involves investment in risky and risk-free assets and uses stochastic differential equations common in quantitative finance, the core contribution relates to reinsurance contract design and risk transfer mechanisms. The mean-variance framework and portfolio allocation aspects have tangential relevance to quantitative finance, but the paper does not address trading strategies, market microstructure, or asset pricing directly.

The paper involves solving high-dimensional coupled extended HJB systems for m insurers and n reinsurers simultaneously. The backward recursive approach with structured matrices (Ψ, H, A, B) across n layers requires careful handling of matrix inversions and recursive relations. The excess-of-loss case involves implicit equations for retention levels and safety loadings that lack closed-form solutions. Numerical implementation would require solving systems of nonlinear equations and handling multi-dimensional optimization with coupling constraints.

The paper provides complete analytical proofs in the appendix, explicit parameter settings for numerical analysis (Section 5), and closed-form solutions for equilibrium strategies. All mathematical derivations are fully detailed. However, no code or computational scripts are provided for reproducing the numerical figures.