Estimation of conditional value-at-risk for input uncertainty with budget allocation

When simulating a complex stochastic system, the behavior of the output response depends on the input parameters estimated from finite real-world data, and the finiteness of data brings input uncertainty to the output response. The quantification of the impact of input uncertainty on output response has been extensively studied. However, most of the existing literature focuses on providing inferences on the mean output response with respect to input uncertainty, including point estimation and confidence interval construction of the mean response. To the best of our knowledge, risk assessment of input uncertainty has been rarely considered. In the present paper, we will introduce risk measures for input uncertainty, study a nested Monte Carlo estimator and construct an asymptotically valid confidence interval for a specific risk measure-Conditional Value-at-Risk of the mean response. We further study the associated budget allocation problem for more efficient nested simulation of the estimator.