Coherent Risk Research under Finite Models

This research in quantitative financial risk management proves that when estimates remain unchanged after replicating all scenarios, binary estimators can accurately describe the same population risk and recover the population dual set from finite models. The study derives Wasserstein, Kolmogorov, and total variation norms under bounded support based on Bernoulli loss risk, characterizes uniform estimability, provides impossibility bounds for arbitrary stochastic estimators, and further derives uniform regret bounds for data-driven risk-averse optimization, with applications in stop-loss retention scenarios.