Monte Carlo integration, quadratic resampling, and asset pricing
The authors consider quasi-Monte Carlo methods for multidimensional numerical integration, with the closed (or half open) \(s\)-dimensional unit cube \(I^s\) as a normalized integration domain. These methods are based on the integration rule \[ \int G(u)du\approx {1\over N}\sum^{N-1}_{n=0} g(x_n) \] with deterministic nodes \(x_i\in\mathbb{R}^s\), which are customarily taken from \(I^s\). To guarantee small integration errors, the nodes should form a low discrepancy point set. A special class of these points is introduced and good parameters in the construction of these points sets are tabulated. In this way, point sets in the \(s\)-dimensional unit cube for \(3\leq s\leq15\) are obtained with very small discrepancy. These special point sets yield excellent numerical results when applied to the quasi-Monte Carlo integration of multivariate Walsh series.
scientific article; zbMATH DE number 792989