  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. We further study the associated budget
allocation problem for efficient nested risk simulation, and finally use a
sharing economy example to illustrate the importance of accessing and
controlling risk due to input uncertainty.
