A confidence interval for tail conditional expectation via two-level simulation

We develop and evaluate a two-level simulation procedure that produces a confidence interval for tail conditional expectation, otherwise known as conditional tail expectation. This risk measure is closely related to conditional value-at-risk, expected shortfall, and worst conditional expectation. The outer level of simulation generates risk factors and the inner level estimates each expected loss conditional on the risk factor. Our procedure uses the statistical theory of empirical likelihood to construct a confidence interval, and it uses tools from the ranking-and-selection literature to make the simulation efficient.