Pareto-optimal reinsurance under dependence uncertainty

Battle Count: 69

The paper is primarily focused on insurance and reinsurance contract design rather than quantitative trading. However, the robust optimization framework, dependence uncertainty handling, and risk measure aggregation techniques (VaR, ES, RVaR) have indirect relevance to portfolio risk management and tail risk assessment in trading contexts. The mathematical techniques for worst-case dependence aggregation could inform robust portfolio construction under model uncertainty.

The theoretical framework involves complex mathematical optimization including: (1) infinite-dimensional to finite-dimensional reduction; (2) minimax optimization over dependence structures; (3) six-case analysis for convex indemnities; (4) asymptotic normality arguments; (5) Makarov bounds for two-dimensional aggregation. Numerical implementation requires solving constrained optimization problems over parameter spaces A1 and A2, computing RVaR integrals, and handling boundary cases. The proofs are technically demanding with multiple case analyses.

The paper provides complete mathematical proofs and detailed numerical examples with specific parameter choices (Pareto distributions with beta=9, lambda=8). However, no code repository is provided. The theoretical results are fully derivable from the proofs given. Numerical optimization procedures are described but not implemented in code. The asymptotic results and Makarov bounds are well-defined and reproducible.