  Nested simulation is a natural approach to tackle nested estimation problems
in operations research and financial engineering. The outer-level simulation
generates outer scenarios and the inner-level simulations are run in each outer
scenario to estimate the corresponding conditional expectation. The resulting
sample of conditional expectations is then used to estimate different risk
measures of interest. Despite its flexibility, nested simulation is notorious
for its heavy computational burden. We introduce a novel simulation procedure
that reuses inner simulation outputs to improve efficiency and accuracy in
solving nested estimation problems. We analyze the convergence rates of the
bias, variance, and MSE of the resulting estimator. In addition, central limit
theorems and variance estimators are presented, which lead to asymptotically
valid confidence intervals for the nested risk measure of interest. We conduct
numerical studies on two financial risk measurement problems. Our numerical
studies show consistent results with the asymptotic analysis and show that the
proposed approach outperforms the standard nested simulation and a state-of-art
regression approach for nested estimation problems.
