Paper Info
Title
On the Error Rate of Conditional Quasi--Monte Carlo for Discontinuous Functions
Abstract
This paper studies the rate of convergence for conditional quasi-Monte Carlo (QMC), which is a counterpart of conditional Monte Carlo. We focus on discontinuous integrands defined on the whole of R-d, which can be unbounded. Under suitable conditions, we show that conditional QMC not only has the smoothing effect (up to infinitely times differentiable) but also can bring orders of magnitude reduction in integration error compared to plain QMC. Particularly, for some typical problems in options pricing and Greeks estimation, conditional randomized QMC that uses n samples yields a mean error of O(n(-1+epsilon)) for arbitrarily small epsilon > 0. As a byproduct, we find that this rate also applies to randomized QMC integration with all terms of the analysis of variance decomposition of the discontinuous integrand, except the one of highest order.
Year
DOI
Venue
2019
10.1137/18M118270X
SIAM JOURNAL ON NUMERICAL ANALYSIS
Keywords
Field
DocType
conditional quasi-Monte Carlo,smoothing,ANOVA decomposition,singularities,discontinuities
Applied mathematics,Monte Carlo method,Valuation of options,Mathematical analysis,Word error rate,Mean squared error,Quasi-Monte Carlo method,Differentiable function,Smoothing,Rate of convergence,Mathematics
Journal
Volume
Issue
ISSN
57
2
0036-1429
Citations 
PageRank 
References 
0
0.34
4
Authors
1
Name
Order
Citations
PageRank
Zhijian He1132.94