An Explicit Cross Entropy Scheme for Mixtures

TL;DR

This paper introduces an explicit iterative scheme combining cross-entropy and EM algorithms to optimize mixture-based importance sampling distributions, addressing nonconvexity issues in complex estimation problems.

Contribution

It presents a novel method for constructing mixture importance sampling distributions that improves over traditional exponential tilting, especially in nonconvex scenarios.

Findings

Effective in estimating rainbow option prices

Addresses nonconvexity in importance sampling

Combines cross-entropy with EM algorithm

Abstract

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.