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. 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. However, risk assessment of the mean response with respect to input uncertainty often plays an important role in system evaluation /controlbecause it quantifies the behavior of the mean response under extreme input models. To the best of our knowledge, it has been rarely systematically studied in the literature. In the present paper, we will fill in the gap and introduce risk measures for input uncertaintyin output analysis. We develop nested Monte Carlo estimators and construct (asymptotically valid) confidence intervals for risk measures of mean response. We further study the associated budget allocation problem for more efficient nested simulation of the estimators, and propose a novel method to solve the problem .
When simulating a complex stochastic system, the behavior of output response depends on input parameters estimated from finite real-world data, and the finiteness of data brings input uncertainty into the system . The quantification of the impact of input uncertainty on output response has been extensively studied. Most of the existing literature focuses on providing inferences on the mean response at the true but unknown input parameter , including point estimation and confidence interval construction . Risk quantification of mean response under input uncertainty often plays an important role in system evaluation and control, because it provides inferences on extreme scenarios of mean response in all possible input models. To the best of our knowledge, it has rarely been systematically studied in the literature. In this paper, first we introduce risk measures of mean response under input uncertainty, and propose a nested Monte Carlo simulation approach to estimate them. Then we develop asymptotical properties such as consistency and asymptotic normality for the proposed nested risk estimators. Finally we study the associated budget allocation problem for efficient nested risk simulation .
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