  Importance sampling has been known as a powerful tool to reduce the variance
of Monte Carlo estimator for rare event simulation. Based on the criterion of
minimizing the variance of Monte Carlo estimator within a parametric family, we
propose a general account for finding the optimal tilting measure. To this end,
when the moment generating function of the underlying distribution exists, we
obtain a simple and explicit expression of the optimal alternative
distribution. The proposed algorithm is quite general to cover many interesting
examples, such as normal distribution, noncentral $\chi^2$ distribution, and
compound Poisson processes. To illustrate the broad applicability of our
method, we study value-at-risk (VaR) computation in financial risk management
and bootstrap confidence regions in statistical inferences.
