A Likelihood Ratio Method for Nested Simulation

Description

Nested simulation has received a considerable amount of attention among simulationresearchers and practitioners in recent years. It finds important applications in the areasof operations research and management science, especially in risk measurement forlarge-scale and complex financial portfolios. In this project, we propose a new simulationmethod, referred to as a likelihood ratio method, for nested simulation. It is expectedthat the proposed method has nice theoretical properties such as consistency and fastrate of convergence. We also study possible improvements for the likelihood ratiomethod, aiming to reduce its variance. One of the directions towards improvementsselects a subset of samples that have smaller conditional variances, and takes the sampleaverage of this subset, rather than using average of all samples. We will provide boththeoretical and practical justifications on why such improved estimators work.We will also consider the extension of the proposed method to other performancemeasures, such as quantiles. By exploiting the connection between the probabilityfunction and the quantile functions, we expect that the likelihood ratio method can alsobe applied for estimating quantiles in principle.