Dynamic reinsurance via martingale transport

Battle Count: 143

The paper is primarily focused on insurance/reinsurance mathematics rather than trading. However, the martingale optimal transport framework and Bass martingale construction have direct connections to robust finance, model-independent pricing, and local volatility calibration. The mathematical tools (Brenier's theorem, Wasserstein distances, martingale couplings) are shared with quantitative finance. The risk measure constraints (VaR, ES) and optimization structure are relevant to risk management in trading contexts, but the specific application domain is insurance.

High complexity due to: (1) requires deep understanding of optimal transport theory, martingale constraints, and stochastic analysis; (2) the Bass martingale construction involves conditional expectations and optimal transport maps; (3) numerical implementation requires solving convex optimization problems in quantile space; (4) the 1-Lipschitz constraint and monotonicity conditions are non-trivial to verify; (5) simulation of pure-jump martingales with prescribed marginals is computationally demanding. However, the final optimization (10) is convex and can be solved efficiently once the framework is set up.

The paper is primarily theoretical with rigorous proofs. Numerical illustrations are provided for specific cases (Cramér-Lundberg model with exponential claims, compensated compound Poisson process). However, no code or computational scripts are provided. The mathematical framework is well-defined and reproducible for researchers with expertise in optimal transport and stochastic analysis. The Bass martingale construction is explicitly given and can be simulated.