A Likelihood Ratio Method for Nested Simulation
Project: Research › GRF
DescriptionNested simulation has received a considerable amount of attention among simulation researchers and practitioners in recent years. It finds important applications in the areas of operations research and management science, especially in risk measurement for large-scale and complex financial portfolios. In this project, we propose a new simulation method, referred to as a likelihood ratio method, for nested simulation. It is expected that the proposed method has nice theoretical properties such as consistency and fast rate of convergence. We also study possible improvements for the likelihood ratio method, aiming to reduce its variance. One of the directions towards improvements selects a subset of samples that have smaller conditional variances, and takes the sample average of this subset, rather than using average of all samples. We will provide both theoretical and practical justifications on why such improved estimators work. We will also consider the extension of the proposed method to other performance measures, such as quantiles. By exploiting the connection between the probability function and the quantile functions, we expect that the likelihood ratio method can also be applied for estimating quantiles in principle.
|Effective start/end date||1/01/18 → …|