Mitigating optimistic bias in entropic risk estimation and optimization

Understand

The entropic risk measure is widely used in high-stakes decision-making across economics, management science, finance, and safety-critical control systems because it captures tail risks associated with uncertain losses.

• However, when data are limited, the empirical entropic risk estimator, formed by replacing the expectation in the risk measure with a sample average, underestimates true risk.
• We show that this negative bias grows superlinearly with the standard deviation of the loss for distributions with unbounded right tails.
• We further demonstrate that several existing bias reduction techniques developed for empirical risk either continue to underestimate entropic risk or substantially overestimate it, potentially leading to overly risky or overly conservative decisions.