Pareto Optimal Centralized Risk Sharing with Multiple Agents: Inclusivity and Fairness

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The paper is primarily focused on insurance and reinsurance design rather than quantitative trading. However, the multiobjective optimization framework, Pareto optimality concepts, and risk measure theory (Expected Shortfall, VaR) have indirect relevance to portfolio risk management and multi-agent financial decision-making. The sequential optimization and balanced representation concepts could theoretically inform multi-strategy allocation or risk-sharing among trading desks, but this is not the paper's focus.

The theoretical framework involves complex multiobjective optimization with sequential matrices, ordered set partitions, convex-group risk measures, and recursive set-valued functions. The number of sequential optimization classes grows combinatorially with agents (d(A_n) follows a recursive formula involving binomial coefficients). Implementing the full characterization for n>3 agents would require handling exponentially many ordered set partitions. The illustrative example with n=2 is tractable but already involves piecewise-defined Expected Shortfall calculations across multiple probability regions.

The paper is purely theoretical with complete mathematical proofs provided in appendices. The illustrative example (Section 5) provides specific numerical parameters (p00=0.1, pa0=0.35, p0b=0.4, pab=0.15, alpha1=0.95, alpha2=0.95, alpha=0.75, theta1=0.5, theta2=0.2) that allow verification of the framework. However, no code or computational implementation is provided. The theoretical results are self-contained with all proofs included.