Monte Carlo integration, quadratic resampling, and asset pricing
type: Item
instance of: scholarly article
title: Monte Carlo integration, quadratic resampling, and asset pricing
zbMATH Open document ID: 0831.65022
DOI: 10.1016/0378-4754(93)E0080-O
author: Jérôme Barraquand
published in: Mathematics and Computers in Simulation
publication date: 1996-02-18T00:00:00Z
review text: 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.
Mathematics Subject Classification ID: 65D32
zbMATH DE Number: 792989
zbMATH Keywords: low-discrepancy point sets
zbMATH Keywords: quasi-Monte Carlo methods
zbMATH Keywords: multidimensional numerical integration
zbMATH Keywords: multivariate Walsh series
reviewed by: Marco Cugiani
MaRDI profile type: Publication
cites work: Numerical Valuation of High Dimensional Multivariate European Securities
cites work: Multi-stage stochastic linear programs for portfolio optimization
cites work: Q5732992
description: scientific article; zbMATH DE number 792989