Orateur
Description
The entropic risk measure is commonly used in high-stakes decision-making to account for tail risks. Empirical entropic risk estimator that replaces expectation in the entropic risk measure with sample average underestimates true risk. To correct this bias, a strongly asymptotically consistent bootstrapping procedure is proposed that fits a distribution to the data and then estimates the bias in the empirical estimator via bootstrapping. Two methods are proposed to fit a distribution to the data, a computationally intensive one that fits the distribution of empirical entropic risk, and a simpler one that fits the tail of the empirical distribution. The approach is applied to a distributionally robust entropic risk minimization problem with type-∞ Wasserstein ambiguity set, demonstrating improved calibration of size of the ambiguity set using debiased validation performance. In an insurance contract design problem, the proposed estimators reduce out-of-sample risk for insurers since they suggest more accurate premiums.
