EVENT DETAILS AND ABSTRACT

Title: Quasi-Monte Carlo Methods for Numerical Integration of Multivariate Functions
Speaker: Fred J. Hickernell
Speaker Info: Hong Kong Baptist University
Brief Description:
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Abstract:

Integration of multivariate functions arises in various applications, such as pricing exotic options. Tensor product rules based on one-dimensional quadrature rules are inefficient for even small values of the dimension, so Monte Carlo methods are often used. However, Monte Carlo methods have two drawbacks: their convergence rate is slow, and the leading constant can increase exponentially with dimension. This talk describes how to understand and overcome these two problems. The convergence rate can be improved by using a low discrepancy sequence instead of simple random sample points. The resulting methods are called quasi-Monte Carlo methods. The convergence rate for Monte Carlo and quasi-Monte Carlo methods becomes essentially independent of dimension when the interactions of many variables together are small enough, and this can be made mathematically precise.