Abstract:
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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.
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