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Activity Number: 651
Type: Contributed
Date/Time: Thursday, August 4, 2016 : 8:30 AM to 10:20 AM
Sponsor: Section on Statistical Computing
Abstract #320820 View Presentation
Title: Guaranteed Adaptive Quasi-Monte Carlo Methods with Control Variates
Author(s): Da Li* and Fred Hickernell
Companies: Illinois Institute of Technology and Illinois Institute of Technology
Keywords: Quasi-Monte Carlo ; Control Variates ; Guaranteed Adaptive Algorithm ; Guaranteed Automatic Integration Library
Abstract:

Recent efforts have been made to construct Quasi-Monte Carlo (QMC) methods for high dimensional integration where the sample size is chosen adaptively to meet some user-defined error tolerance. These algorithms have theoretical guarantees. Our work focuses on extending these adaptive QMC methods to accommodate control variates, especially since control variates with optimal coefficients always reduce the number of samples required. One challenge is that the optimal control variate coefficient for QMC is generally not the same as for IID Monte Carlo, as explained by Hickernell, Lemieux, and Owen, Control Variates for Quasi-Monte Carlo, Statistical Science, 2005. In this talk we show how to choose the right control variate coefficient while reliably bounding the sampling error. The extra computational cost required for using control variates is minimal. We demonstrate the reduction in computational cost that can be achieved by our new algorithm with some option pricing examples.


Authors who are presenting talks have a * after their name.

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