Asymptotic Analysis of Optimal Diversification in Catastrophe Risk Pooling

Battle Count: 77

The paper is primarily focused on insurance and catastrophe risk management rather than quantitative trading. However, the heavy-tailed distribution theory, VaR-based risk measures, and diversification concepts have some overlap with portfolio risk management. The asymptotic analysis techniques and optimization methods could be tangentially relevant to tail risk management in trading portfolios, but the direct application to trading strategies is minimal.

The theoretical framework requires understanding of regular variation, extreme value theory, and multi-objective optimization. The asymptotic optimal pool has a closed-form solution (Theorem 2.3) which simplifies implementation. However, the practical optimization requires GSA or similar algorithms with significant computational cost. The empirical analysis involves multiple statistical tests (tail index estimation, independence tests, tail equivalence tests) and EVT-based quantile estimation. The R implementation is feasible but requires actuarial/statistical expertise.

The paper provides detailed simulation parameters (Fréchet distributions with specific parameters, 1 million observations, 50 samples, specific p-values tested), uses publicly available NFIP data, and specifies the GSA algorithm via the R package GenSA. However, no code repository is provided. The theoretical derivations are fully presented with proofs in appendices.