Paper Info
Title
Quasi-Monte Carlo for discontinuous integrands with singularities along the boundary of the unit cube.
Abstract
This paper studies randomized quasi-Monte Carlo (QMC) sampling for discontinuous integrands having singularities along the boundary of the unit cube [0, 1](d). Both discontinuities and singularities are extremely common in the pricing and hedging of financial derivatives and have a tremendous impact on the accuracy of QMC. It was previously known that the root mean square error of randomized QMC is only o(n(1/2)) for discontinuous functions with singularities. We find that under some mild conditions, randomized QMC yields an expected error of O(n(-1/2-1/(4d-2)+epsilon)) for arbitrarily small epsilon > 0. Moreover, one can get a better rate if the boundary of discontinuities is parallel to some coordinate axes. As a by-product, we find that the expected error rate attains O(n(-1+)(epsilon)) if the discontinuities are QMC-friendly, in the sense that all the discontinuity boundaries are parallel to coordinate axes. The results can be used to assess the QMC accuracy for some typical problems from financial engineering.
Year
DOI
Venue
2018
10.1090/mcom/3324
MATHEMATICS OF COMPUTATION
Keywords
Field
DocType
Quasi-Monte Carlo methods,singularities,discontinuities
Classification of discontinuities,Mathematical analysis,Quasi-Monte Carlo method,Gravitational singularity,Unit cube,Mathematics
Journal
Volume
Issue
ISSN
87
314
0025-5718
Citations 
PageRank 
References 
0
0.34
4
Authors
1
Name
Order
Citations
PageRank
Zhijian He1132.94