  The key issue in importance sampling is the choice of the alternative
sampling distribution, which is often chosen from the exponential tilt family
of the underlying distribution. However, when the problem exhibits certain kind
of nonconvexity, it is very likely that a single exponential change of measure
will never attain asymptotic optimality and can lead to erroneous estimates. In
this paper we introduce an explicit iterative scheme which combines the
traditional cross-entropy method and the EM algorithm to find an efficient
alternative sampling distribution in the form of mixtures. We also study the
applications of this scheme to the estimation of rainbow option prices.
