Presentation on YouTube.

When faced with multiple options, it is observed that a decision-maker may select a certain option that gives a higher expected loss than a lottery (gamble over the options). To account for risk aversion, the entropic risk measure is widely used in the literature as it is a convex law-invariant risk measure. In real-world applications, a decision maker does not know the true distribution of the uncertain parameter and has access to only a finite number of samples. It is well known that the average risk computed with the finite number of samples underestimates the true entropic risk, which defies the purpose of using risk measures to protect decision makers. We introduce two procedures based on optimal transport and extreme value theory that learn Gaussian mixture models and then use bootstrapping to identify scaling parameters that correct the bias in the estimation of the entropic risk. Furthermore, we study a distributionally robust optimization problem with entropic risk measure and use debiasing in the cross-validation procedure to tune the radius (hyperparameter) of the ambiguity set. Using our debiasing approach, we are able to achieve lower risk in project selection, portfolio optimization, and insurance pricing problems.