Distributionally Robust Insurance under Bregman-Wasserstein Divergence

Battle Count: 64

The paper is primarily focused on insurance contract design and actuarial risk management rather than quantitative trading. However, the Bregman-Wasserstein divergence framework and distributionally robust optimization methodology have conceptual parallels with robust portfolio optimization (the paper references Blanchet et al. 2022's robust mean-variance framework). The asymmetric penalization of deviations and worst-case risk measure minimization techniques could inform robust trading strategies under model uncertainty, but direct applicability to trading is limited.

The theoretical framework involves advanced mathematical tools including optimal transport theory, Bregman divergences, Lagrangian duality, minimax theorems, and modification arguments. The closed-form solutions for Problem 1 are relatively tractable, but Problem 2 requires solving a nested optimization with Lagrangian multipliers (lambda*, beta*) and a constructive modification procedure for the worst-case survival function. Numerical implementation requires careful handling of the piecewise-defined optimal indemnity functions and the flat-segment modification at the VaR quantile. The TVaR example involves multiple sub-cases depending on parameter regimes.

The paper provides complete closed-form analytical solutions and detailed proofs in the appendix. Numerical examples are provided with specific parameter settings (truncated exponential distribution, specific Bregman generators). However, no code or computational scripts are provided. The theoretical results are fully reproducible from the mathematical derivations, but numerical reproduction would require implementing the optimization algorithms described.