A cross-entropy scheme for mixtures

Abstract

We discuss how to generalize the classic cross-entropy method in the case where a family of mixture distributions, such as the mixture of multiple Gaussian modes, is used as an importance sampling distribution. A new iterative cross-entropy scheme, based on the idea of the EM method, is proposed to overcome the challenge of deciding the optimal weights for each mode in the mixture. Detailed studies of this new algorithm and its applications to the estimation of rainbow option prices are presented to demonstrate the efficiency of the scheme.